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Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 12th Standard HSC Maharashtra State Board chapter 3 - Trigonometric Functions [Latest edition]

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Mathematics and Statistics 1 (Arts and Science) 12th Standard HSC Maharashtra State Board - Shaalaa.com

Chapter 3: Trigonometric Functions

Exercise 3.1Exercise 3.2Exercise 3.3Miscellaneous exercise - 3

Exercise 3.1 [Page 75]

Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 12th Standard HSC Maharashtra State Board Chapter 3 Trigonometric Functions Exercise 3.1 [Page 75]

Exercise 3.1 | Q 1.1 | Page 75

Find the principal solution of the following equation: 

cosθ = `(1)/(2)`

Exercise 3.1 | Q 1.2 | Page 75

Find the principal solution of the following equation: 

Secθ = `(2)/sqrt(3)`

Exercise 3.1 | Q 1.3 | Page 75

Find the principal solution of the following equation :

cotθ = √3

Exercise 3.1 | Q 1.4 | Page 75

Find the principal solution of the following equation:

cotθ = 0

Exercise 3.1 | Q 2.1 | Page 75

Find the principal solution of the following equation:

sin θ = `-1/2`

Exercise 3.1 | Q 2.2 | Page 75

Find the principal solution of the following equation: 

tan θ = – 1

Exercise 3.1 | Q 2.3 | Page 75

Find the principal solution of the following equation:

`sqrt(3)`cosecθ+ 2 = 0 

Exercise 3.1 | Q 3.1 | Page 75

Find the general solution of the following equation:

sinθ = `1/2`.

Exercise 3.1 | Q 3.2 | Page 75

Find the general solution of the following equation :

cosθ = `sqrt(3)/(2)`

Exercise 3.1 | Q 3.3 | Page 75

Find the general solution of the following equation:

tan θ = `(1)/(sqrt(3))`

Exercise 3.1 | Q 3.4 | Page 75

Find the general solution of the following equation:

cot θ = 0.

Exercise 3.1 | Q 4.1 | Page 75

Find the general solution of the following equation:

sec θ = `sqrt(2)`.

Exercise 3.1 | Q 4.2 | Page 75

Find the general solution of the following equation:

cosec θ = - √2.

Exercise 3.1 | Q 4.3 | Page 75

Find the general solution of the following equation:

tan θ = - 1

Exercise 3.1 | Q 5.1 | Page 75

Find the general solution of the following equation:

sin 2θ = `1/2`

Exercise 3.1 | Q 5.2 | Page 75

Find the general solution of the following equation:

tan `(2θ)/(3)` = √3.

Exercise 3.1 | Q 5.3 | Page 75

Find the general solution of the following equation:

cot 4θ = – 1

Exercise 3.1 | Q 6.1 | Page 75

Find the general solution of the following equation:

4cos2θ  = 3.

Exercise 3.1 | Q 6.2 | Page 75

Find the general solution of the following equation:

4sin2θ = 1.

Exercise 3.1 | Q 6.3 | Page 75

Find the general solution of the following equation:

cos 4θ = cos 2θ

Exercise 3.1 | Q 7.1 | Page 75

Find the general solution of the following equation:

sin θ = tan θ.

Exercise 3.1 | Q 7.2 | Page 75

Find the general solution of the following equation: 

tan3θ = 3 tanθ.

Exercise 3.1 | Q 7.3 | Page 75

Find the general solution of the following equation:

cos θ + sin θ = 1.

Exercise 3.1 | Q 8.1 | Page 75

State whether the following equation have solution or not?

cos 2θ = – 1

Exercise 3.1 | Q 8.2 | Page 75

State whether the following equation has a solution or not?

cos2θ = – 1.

Exercise 3.1 | Q 8.3 | Page 75

State whether the following equation has a solution or not?

2sinθ = 3

Exercise 3.1 | Q 8.4 | Page 75

State whether the following equation have solution or not?

3 tanθ = 5

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Exercise 3.2 [Page 88]

Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 12th Standard HSC Maharashtra State Board Chapter 3 Trigonometric Functions Exercise 3.2 [Page 88]

Exercise 3.2 | Q 1.1 | Page 88

Find the Cartesian co-ordinates of the point whose polar co-ordinates are :

`(sqrt(2), pi/4)`

Exercise 3.2 | Q 1.2 | Page 88

Find the Cartesian co-ordinates of the point whose polar co-ordinates are :

`(4,  pi/2)`

Exercise 3.2 | Q 1.3 | Page 88

Find the Cartesian co-ordinates of the point whose polar co-ordinates are:

`(3/4, (3pi)/4)`

Exercise 3.2 | Q 1.4 | Page 88

Find the Cartesian co-ordinates of the point whose polar co-ordinates are:

`(1/2, (7pi)/3)`

Exercise 3.2 | Q 2.1 | Page 88

Find the polar co-ordinates of the point whose Cartesian co-ordinates are.

`(sqrt(2), sqrt(2))`

Exercise 3.2 | Q 2.2 | Page 88

Find the polar co-ordinates of the point whose Cartesian co-ordinates are.

`(0, 1/2)`

Exercise 3.2 | Q 2.3 | Page 88

Find the polar co-ordinates of the point whose Cartesian co-ordinates are.

(1, - √3)

Exercise 3.2 | Q 2.4 | Page 88

Find the polar co-ordinates of the point whose Cartesian co-ordinates are.

`(3/2, (3√3)/2)`.

Exercise 3.2 | Q 3 | Page 88

In ΔABC, if ∠A = 45°, ∠B = 60° then find the ratio of its sides.

Exercise 3.2 | Q 4 | Page 88

In Δ ABC, prove that `sin(("B - C")/2) = (("b - c")/2)cos  "A"/(2)`.

Exercise 3.2 | Q 5 | Page 88

With the usual notations prove that `2{asin^2  "C"/(2) + "c"sin^2  "A"/(2)}` = a – b + c.

Exercise 3.2 | Q 6 | Page 88

In Δ ABC, prove that a3 sin(B – C) + b3sin(C – A) + c3sin(A – B) = 0

Exercise 3.2 | Q 7 | Page 88

In ΔABC, if cot A, cot B, cot C are in A.P. then show that a2, b2, c2 are also in A.P.

Exercise 3.2 | Q 8 | Page 88

In ΔABC, if a cos A = b cos B then prove that the triangle is either a right angled or an isosceles traingle.

Exercise 3.2 | Q 9 | Page 88

With usual notations prove that 2(bc cosA + ac cosB + ab cosC) = a2 + b2 + c.

Exercise 3.2 | Q 10.1 | Page 88

In ΔABC, if a = 18, b = 24, c = 30 then find the values of cosA

Exercise 3.2 | Q 10.2 | Page 88

In ΔABC, if a = 18, b = 24, c = 30 then find the values of sin `A/2`.

Exercise 3.2 | Q 10.3 | Page 88

In ΔABC, if a = 18, b = 24, c = 30 then find the values of cos `A/2`

Exercise 3.2 | Q 10.4 | Page 88

In ΔABC, if a = 18, b = 24, c = 30 then find the values of tan `A/2`

Exercise 3.2 | Q 10.5 | Page 88

In ΔABC, if a = 18, b = 24, c = 30 then find the values of A(ΔABC)

Exercise 3.2 | Q 10.6 | Page 88

In ΔABC, if a = 18, b = 24, c = 30 then find the values of sinA

Exercise 3.2 | Q 11 | Page 88

In ΔABC prove that `(b + c - a) tan  "A"/(2) = (c + a - b)tan  "B"/(2) = (a + b - c)tan  "C"/(2)`.

Exercise 3.2 | Q 12 | Page 88

In ΔABC prove that `sin  "A"/(2). sin  "B"/(2). sin  "C"/(2) = ["A(ΔABC)"]^2/"abcs"`

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Exercise 3.3 [Pages 102 - 103]

Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 12th Standard HSC Maharashtra State Board Chapter 3 Trigonometric Functions Exercise 3.3 [Pages 102 - 103]

Exercise 3.3 | Q 1.1 | Page 102

Find the principal value of the following: `sin^-1 (1/2)`

Exercise 3.3 | Q 1.2 | Page 102

Find the principal value of the following: cosec- 1(2)

Exercise 3.3 | Q 1.3 | Page 102

Find the principal value of the following: tan-1(– 1)

Exercise 3.3 | Q 1.4 | Page 102

Find the principal value of the following: tan- 1( - √3)

Exercise 3.3 | Q 1.5 | Page 102

Find the principal value of the following: sin-1 `(1/sqrt(2))`

Exercise 3.3 | Q 1.6 | Page 102

Find the principal value of the following: cos- 1`(-1/2)`

Exercise 3.3 | Q 2.1 | Page 102

Evaluate the following:

`tan^-1(1) + cos^-1(1/2) + sin^-1(1/2)`

Exercise 3.3 | Q 2.2 | Page 102

Evaluate the following:

`cos^-1(1/2) + 2sin^-1(1/2)`

Exercise 3.3 | Q 2.3 | Page 102

Evaluate the following:

`tan^-1 sqrt(3) - sec^-1 (-2)`

Exercise 3.3 | Q 2.4 | Page 103

Evaluate the following:

`"cosec"^-1(-sqrt(2)) + cot^-1(sqrt(3))`

Exercise 3.3 | Q 3.1 | Page 103

Prove the following: 

`sin^-1(1/sqrt(2)) -3sin^-1(sqrt(3)/2) = -(3pi)/(4)`

Exercise 3.3 | Q 3.2 | Page 103

Prove the following:

`sin^-1(-1/2) + cos^-1(-sqrt(3)/2) = cos^-1(-1/2)`

Exercise 3.3 | Q 3.3 | Page 103

Prove the following:

`sin^-1(3/5) + cos^-1(12/13) = sin^-1(56/65)`

Exercise 3.3 | Q 3.4 | Page 103

Prove the following:

`cos^-1(3/5) + cos^-1(4/5) = pi/(2)`

Exercise 3.3 | Q 3.5 | Page 103

Prove the following:

`tan^-1(1/2) + tan^-1(1/3) = pi/(4)`

Exercise 3.3 | Q 3.6 | Page 103

Prove the following: 

`2tan^-1(1/3) = tan^-1(3/4)`

Exercise 3.3 | Q 3.7 | Page 103

Prove the following:

`tan^-1["cosθ + sinθ"/"cosθ - sinθ"] = pi/(4) + θ, if θ ∈ (- pi/4, pi/4)`

Exercise 3.3 | Q 3.8 | Page 103

Prove the following:

`tan^-1[sqrt((1 - cosθ)/(1 + cosθ))] = θ/(2)`, if θ ∈ (– π, π).

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Miscellaneous exercise - 3 [Pages 106 - 108]

Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 12th Standard HSC Maharashtra State Board Chapter 3 Trigonometric Functions Miscellaneous exercise - 3 [Pages 106 - 108]

Miscellaneous exercise - 3 | Q 1.01 | Page 106

Select the correct option from the given alternatives:

The principal solutions of equation sin θ = `- 1/2` are

  • `(5pi)/6, pi/6`

  • `(7pi)/6, (11pi)/6`

  • `pi/6, (7pi)/6`

  • `(7pi)/6, pi/3`

Miscellaneous exercise - 3 | Q 1.02 | Page 106

Select the correct option from the given alternatives:

The principal solutions of equation cot θ = `sqrt3` are

  • `pi/6, (7pi)/6`

  • `pi/6, (5pi)/6`

  • `pi/6, (8pi)/6`

  • `(7pi)/6, pi/3`

Miscellaneous exercise - 3 | Q 1.03 | Page 106

Select the correct option from the given alternatives:

The general solution of sec x = `sqrt2` is

  • `2"n"pi +- pi/4, "n" ∈ "Z"`

  • `2"n"pi +- pi/2, "n" ∈ "Z"`

  • `"n"pi +- pi/2, "n" ∈ "Z"`

  • `2"n"pi +- pi/3, "n" ∈ "Z"`

Miscellaneous exercise - 3 | Q 1.04 | Page 106

Select the correct option from the given alternatives:

If cos pθ = cos qθ, p ≠ q, then,

  • θ = `(2"n"pi)/("p" +- "q")`

  • θ = 2nπ

  • θ - 2nπ ± p

  • θ = nπ ± q

Miscellaneous exercise - 3 | Q 1.05 | Page 106

Select the correct option from the given alternatives:

If polar coordinates of a point are `(2, pi/4)`, then its cartesian coordinates are

  • `(2, sqrt2)`

  • `(sqrt2, 2)`

  • (2, 2)

  • `(sqrt2, sqrt2)`

Miscellaneous exercise - 3 | Q 1.06 | Page 106

Select the correct option from the given alternatives:

If `sqrt3`cos x - sin x = 1, then general value of x is

  • `2"n"pi +- pi/3`

  • `2"n"pi +- pi/6`

  • `2"n"pi +- pi/3 - pi/6`

  • `"n"pi + (- 1)^"n" pi/3`

Miscellaneous exercise - 3 | Q 1.07 | Page 107

Select the correct option from the given alternatives:

In Δ ABC if ∠A = 45°, ∠B = 60°, then the ratio of its sides are

  • `2 : sqrt6 : sqrt3 + 1`

  • `sqrt2 : 2 : sqrt3 + 1`

  • `2sqrt2 : sqrt2 : sqrt3`

  • `2 : 2sqrt2 : sqrt3 + 1`

Miscellaneous exercise - 3 | Q 1.08 | Page 107

Select the correct option from the given alternatives:

In ΔABC if c2 + a2 - b2 = ac, then ∠B = ____

  • `pi/4`

  • `pi/3`

  • `pi/2`

  • `pi/6`

Miscellaneous exercise - 3 | Q 1.09 | Page 107

Select the correct option from the given alternatives:

In ΔABC, ac cos B - bc cos A = _______

  • a2 - b2 

  • b2 - c2 

  • c2 - a2 

  • a2 - b2 - c2 

Miscellaneous exercise - 3 | Q 1.1 | Page 107

Select the correct option from the given alternatives:

If in a triangle, the angles are in A.P. and b: c = √3: √2, then A is equal to

  • 30°

  • 60°

  • 75°

  • 45°

Miscellaneous exercise - 3 | Q 1.11 | Page 107

Select the correct option from the given alternatives:

`"cos"^-1 ("cos" (7pi)/6)` = _________.

  • `(7pi)/6`

  • `(5pi)/6`

  • `pi/6`

  • `(3pi)/2`

Miscellaneous exercise - 3 | Q 1.12 | Page 107

Select the correct option from the given alternatives:

The value of cot (tan-12x + cot-12x) is

  • 0

  • 2x

  • π + 2x

  • π - 2x

Miscellaneous exercise - 3 | Q 1.13 | Page 107

Select the correct option from the given alternatives:

The principal value of sin-1 `(- sqrt3/2)` is

  • `(- (2pi)/3)`

  • `(4pi)/3`

  • `(5pi)/3`

  • `- pi/3`

Miscellaneous exercise - 3 | Q 1.14 | Page 107

Select the correct option from the given alternatives:

If `"sin"^-1 4/5 + "cos"^-1 12/13 = "sin"^-1 alpha`, then α = ______

  • `63/65`

  • `62/65`

  • `61/65`

  • `60/65`

Miscellaneous exercise - 3 | Q 1.15 | Page 107

Select the correct option from the given alternatives:

If tan-1(2x) + tan-1(3x) = `pi/4`, then x = _____

  • - 1

  • `1/6`

  • `2/6`

  • `3/2`

Miscellaneous exercise - 3 | Q 1.16 | Page 108

Select the correct option from the given alternatives:

`2 "tan"^-1 (1/3) + "tan"^-1 (1/7) =` _____

  • `"tan"^-1(4/5)`

  • `pi/2`

  • 1

  • `pi/4`

Miscellaneous exercise - 3 | Q 1.17 | Page 108

Select the correct option from the given alternatives:

`"tan"(2"tan"^-1 (1/5) - pi/4)` = ______

  • `17/7`

  • `-17/7`

  • `7/17`

  • `-7/17`

Miscellaneous exercise - 3 | Q 1.18 | Page 108

Select the correct option from the given alternatives:

The principal value branch of sec-1x is

  • `[-pi/2, pi/2] - {0}`

  • `[0, pi] - {pi/2}`

  • (0, π)

  • `(- pi/2, pi/2)`

Miscellaneous exercise - 3 | Q 1.19 | Page 108

Select the correct option from the given alternatives:

`"cos"["tan"^-1 1/3 + "tan"^-1 1/2]` = ______

  • `1/sqrt2`

  • `sqrt3/2`

  • `1/2`

  • `pi/4`

Miscellaneous exercise - 3 | Q 1.2 | Page 108

Select the correct option from the given alternatives:

If tan θ + tan 2θ + tan 3θ = tan θ.tan 2θ. tan 3θ, then the general value of the θ is

  • `("n"pi)/6`

  • `"n"pi +- pi/4`

  • `("n"pi)/2`

Miscellaneous exercise - 3 | Q 1.21 | Page 108

Select the correct option from the given alternatives:

In any ΔABC, if acos B = bcos A, then the triangle is

  • equilateral triangle

  • isosceles triangle

  • scalene

  • right-angled

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Miscellaneous exercise - 3 [Pages 108 - 111]

Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 12th Standard HSC Maharashtra State Board Chapter 3 Trigonometric Functions Miscellaneous exercise - 3 [Pages 108 - 111]

Miscellaneous exercise - 3 | Q 1.1 | Page 108

Find the principal solutions of the following equation:

sin 2θ = - `1/2`

Miscellaneous exercise - 3 | Q 1.2 | Page 108

Find the principal solutions of the following equation:

tan 3θ = - 1

Miscellaneous exercise - 3 | Q 1.3 | Page 108

Find the principal solutions of the following equation:

cot θ = 0

Miscellaneous exercise - 3 | Q 2.1 | Page 108

Find the principal solutions of the following equation:

sin 2θ = `- 1/(√2)`.

Miscellaneous exercise - 3 | Q 2.2 | Page 108

Find the principal solutions of the following equation:
tan 5θ = -1

Miscellaneous exercise - 3 | Q 2.3 | Page 108

Find the principal solutions of the following equation:

cot 2θ = 0.

Miscellaneous exercise - 3 | Q 3.1 | Page 109

State whether the following equation has a solution or not?

cos 2θ = `1/3`

Miscellaneous exercise - 3 | Q 3.2 | Page 109

State whether the following equation has a solution or not?

cos2θ = – 1.

Miscellaneous exercise - 3 | Q 3.3 | Page 109

State whether the following equation has a solution or not?

2sinθ = 3

Miscellaneous exercise - 3 | Q 3.4 | Page 109

State whether the following equation has a solution or not?

3 sin θ = 5.

Miscellaneous exercise - 3 | Q 4.1 | Page 109

Find the general solutions of the following equation:

`tan theta = - sqrt3`

Miscellaneous exercise - 3 | Q 4.2 | Page 109

Find the general solutions of the following equation:

`tan^2 theta = 3`

Miscellaneous exercise - 3 | Q 4.3 | Page 109

Find the general solutions of the following equation:

sin θ - cos θ = 1

Miscellaneous exercise - 3 | Q 4.4 | Page 109

Find the general solutions of the following equation:

sin2 θ - cos2 θ = 1

Miscellaneous exercise - 3 | Q 5 | Page 109

In Δ ABC, prove that `cos(("A" - "B")/2) = (("a" + "b")/"c")sin  "C"/2` .

Miscellaneous exercise - 3 | Q 6 | Page 109

With the usual notations, prove that `(sin("A" - "B"))/(sin ("A" + "B")) = ("a"^2 - "b"^2)/"c"^2`

Miscellaneous exercise - 3 | Q 7 | Page 109

In ΔABC, prove that `("a - b")^2 cos^2  "C"/2 + ("a + b")^2 sin^2  "C"/2 = "c"^2`

Miscellaneous exercise - 3 | Q 8 | Page 109

In Δ ABC, if cos A = sin B - cos C then show that it is a right-angled triangle.

Miscellaneous exercise - 3 | Q 9 | Page 109

If `(sin "A")/(sin "C") = (sin ("A - B"))/(sin ("B - C"))`, then show that a2, b2, c2 are in A.P.

Miscellaneous exercise - 3 | Q 10 | Page 109

Solve the triangle in which a = `(sqrt3 + 1)`, b = `(sqrt3 - 1)` and ∠C = 60°.

Miscellaneous exercise - 3 | Q 11.1 | Page 109

In any Δ ABC, prove the following:

a sin A - b sin B = c sin (A - B)

Miscellaneous exercise - 3 | Q 11.2 | Page 109

In any Δ ABC, prove the following:

`("c" - "b cos A")/("b" - "c cos A") = ("cos B")/("cos C")`

Miscellaneous exercise - 3 | Q 11.3 | Page 109

In any Δ ABC, prove the following:

a2 sin (B - C) = (b2 - c2) sin A.

Miscellaneous exercise - 3 | Q 11.4 | Page 109

In any Δ ABC, prove the following:

ac cos B - bc cos A = a2 - b2

Miscellaneous exercise - 3 | Q 11.5 | Page 109

In any Δ ABC, prove the following:

`"cos A"/"a" + "cos B"/"b" + "cos C"/"c" = ("a"^2 + "b"^2 + "c"^2)/(2"abc")`

Miscellaneous exercise - 3 | Q 11.6 | Page 109

In any Δ ABC, prove the following:

`"cos 2A"/"a"^2 - "cos 2B"/"b"^2 = 1/"a"^2 - 1/"b"^2`

Miscellaneous exercise - 3 | Q 11.7 | Page 109

In any Δ ABC, prove the following:

`("b" - "c")/"a" = (tan  "B"/2 - tan  "C"/2)/(tan  "B"/2 +tan  "C"/2)`

Miscellaneous exercise - 3 | Q 12 | Page 109

In Δ ABC, if a, b, c are in A.P., then show that cot `"A"/2, cot  "B"/2, cot  "C"/2` are also in A.P.

Miscellaneous exercise - 3 | Q 13 | Page 109

In Δ ABC, if ∠C = 90°, then prove that sin (A - B) = `("a"^2 - "b"^2)/("a"^2 + "b"^2)`

Miscellaneous exercise - 3 | Q 14 | Page 110

In Δ ABC, if `"cos A"/"a" = "cos B"/"b"`, then show that it is an isosceles triangle.

Miscellaneous exercise - 3 | Q 15 | Page 110

In Δ ABC, if sin2 A + sin2 B = sin2 C, then show that the triangle is a right-angled triangle.

Miscellaneous exercise - 3 | Q 16 | Page 110

In Δ ABC, prove that a2 (cos2 B - cos2 C) + b2 (cos2 C - cos2 A) + c2 (cos2 A - cos2 B) = 0.

Miscellaneous exercise - 3 | Q 17 | Page 110

With the usual notations, show that
(c2 - a2 + b2) tan A = (a2 - b2 + c2) tan B = (b2 - c2 + a2) tan C

Miscellaneous exercise - 3 | Q 18 | Page 110

In Δ ABC, if a cos2 `"C"/2 + "c cos"^2 "A"/2 = "3b"/2`, then prove that a, b, c are in A.P.

Miscellaneous exercise - 3 | Q 19 | Page 110

Show that `2 sin^-1 (3/5) = tan^-1(24/7)`

Miscellaneous exercise - 3 | Q 20 | Page 110

Show that

`tan^-1(1/5) + tan^-1(1/7) + tan^-1(1/3) + tan^-1 (1/8) = pi/4.`

Miscellaneous exercise - 3 | Q 21 | Page 110

Prove that `tan^-1 sqrt"x" = 1/2 cos^-1 ((1 - "x")/(1 + "x"))`, if x ∈ [0, 1]

Miscellaneous exercise - 3 | Q 22 | Page 110

Show that `(9pi)/8 - 9/4 sin^-1 (1/3) = 9/4 sin^-1 ((2sqrt2)/3)`.

Miscellaneous exercise - 3 | Q 23 | Page 110

Show that `tan^-1  ((sqrt(1 + "x") - sqrt(1 - "x"))/(sqrt(1 + "x") + sqrt(1 - "x"))) = pi/4 - 1/2 cos^-1 "x"`, for `- 1/sqrt2 <= "x" <= 1`

Miscellaneous exercise - 3 | Q 24 | Page 110

If sin `(sin^-1  1/5 + cos^-1 x) = 1`, then find the value of x.

Miscellaneous exercise - 3 | Q 25 | Page 110

If `tan^-1 (("x" - 1)/("x" - 2)) + tan^-1 (("x" + 1)/("x" + 2)) = pi/4`, find the value of x.

Miscellaneous exercise - 3 | Q 26 | Page 110

If 2 tan-1(cos x) = tan-1(2 cosec x), then find the value of x.

Miscellaneous exercise - 3 | Q 27 | Page 110

Solve: `tan^-1 ("1 - x"/"1 + x") = 1/2 (tan^-1 "x")`, for x > 0.

Miscellaneous exercise - 3 | Q 28 | Page 110

If sin-1(1 - x) - 2 sin-1x =  `pi/2`, then find the value of x.

Miscellaneous exercise - 3 | Q 29 | Page 110

If tan-12x + tan-13x = `pi/4`, then find the value of x.

Miscellaneous exercise - 3 | Q 30 | Page 110

Show that `tan^-1  1/2 - tan^-1  1/4 = tan^-1  2/9`.

Miscellaneous exercise - 3 | Q 31 | Page 110

Show that `cot^-1  1/3 - tan^-1  1/3 = cot^-1  3/4`.

Miscellaneous exercise - 3 | Q 32 | Page 110

Show that `tan^-1  1/2 = 1/3  tan^-1  11/2`

Miscellaneous exercise - 3 | Q 33 | Page 111

Show that `cos^-1  sqrt3/2 + 2 sin^-1  sqrt3/2 = (5pi)/6`.

Miscellaneous exercise - 3 | Q 34 | Page 111

Show that `2 cot^-1  3/2 +  sec^-1  13/12 = pi/2`

Miscellaneous exercise - 3 | Q 35.1 | Page 111

Prove the following:

`cos^-1 "x" = tan^-1 (sqrt(1 - "x"^2)/"x")`, if x > 0

Miscellaneous exercise - 3 | Q 35.2 | Page 111

Prove the following:

`cos^-1 "x" = pi + tan^-1 (sqrt(1 - "x"^2)/"x")`, if x < 0

Miscellaneous exercise - 3 | Q 36 | Page 111

If | x | < 1, then prove that

`2 tan^-1 "x" = tan^-1 ("2x"/(1 - "x"^2)) = sin^-1 ("2x"/(1 + "x"^2)) = cos^-1 ((1 - "x"^2)/(1 + "x"^2))`

Miscellaneous exercise - 3 | Q 37 | Page 111

If x, y, z are positive, then prove that

`tan^-1 (("x - y")/(1 + "xy")) + tan^-1 (("y - z")/(1 + "yz")) + tan^-1 (("z - x")/(1 + "zx")) = 0`

Miscellaneous exercise - 3 | Q 38 | Page 111

If `tan^-1 "x" + tan^-1 "y" + tan^-1 "z" = pi/2,` then show that xy + yz + zx = 1

Miscellaneous exercise - 3 | Q 39 | Page 111

If cos-1 x + cos-1y + cos-1z = 3π, then show that x2 + y2 + z2 + 2xyz = 1.

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Chapter 3: Trigonometric Functions

Exercise 3.1Exercise 3.2Exercise 3.3Miscellaneous exercise - 3
Mathematics and Statistics 1 (Arts and Science) 12th Standard HSC Maharashtra State Board - Shaalaa.com

Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 12th Standard HSC Maharashtra State Board chapter 3 - Trigonometric Functions

Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 12th Standard HSC Maharashtra State Board chapter 3 (Trigonometric Functions) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board Mathematics and Statistics 1 (Arts and Science) 12th Standard HSC Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics and Statistics 1 (Arts and Science) 12th Standard HSC Maharashtra State Board chapter 3 Trigonometric Functions are Trigonometric Equations and Their Solutions, Solutions of Triangle, Inverse Trigonometric Functions.

Using Balbharati 12th Board Exam solutions Trigonometric Functions exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Balbharati Solutions are important questions that can be asked in the final exam. Maximum students of Maharashtra State Board 12th Board Exam prefer Balbharati Textbook Solutions to score more in exam.

Get the free view of chapter 3 Trigonometric Functions 12th Board Exam extra questions for Mathematics and Statistics 1 (Arts and Science) 12th Standard HSC Maharashtra State Board and can use Shaalaa.com to keep it handy for your exam preparation

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