# SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 1 - Trigonometric Functions [Latest edition]

## Chapter 1: Trigonometric Functions

MCQ

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 1 Trigonometric FunctionsMCQ

#### 2 marks each

MCQ | Q 1

The principal solutions of sqrt(3) sec x − 2 = 0 are ______

• pi/3, (11pi)/6

• pi/6, (11pi)/6

• pi/4, (11pi)/4

• pi/6, (11pi)/3

MCQ | Q 2

In ∆ABC, if cos A = (sin"B")/(2 sin "C"), then ∆ABC is ______

• an equilateral triangle

• a right angled triangle

• an isosceles triangle

• an isosceles right angled triangle

MCQ | Q 3

sin−1x − cos−1x = pi/6, then x = ______

• 1/2

• sqrt(3)/2

• -1/2

• -sqrt(3)/2

MCQ | Q 4

The principal value of sin−1(1/2) is ______

• pi/3

• pi/6

• (2pi)/3

• (3pi)/2

MCQ | Q 5

The principal value of cos−1(-1/2) is ______

• pi/3

• pi/6

• (2pi)/3

• (3pi)/2

MCQ | Q 6

In ∆ABC, if ∠A = 30°, ∠B = 60°, then the ratio of sides is ______

• 1:sqrt(3):2

• 2:sqrt(3):1

• sqrt(3):1:2

• sqrt(3):2:1

MCQ | Q 7

In ∆ABC, if b2 + c2 − a2 = bc, then ∠A = ______

• pi/4

• pi/3

• pi/2

• pi/6

MCQ | Q 8

If polar co-ordinates of a point are (3/4, (3pi)/4), then its Cartesian co-ordinate are ______

• (3/(4sqrt(2)), -3/(4sqrt(2)))

• (3/(4sqrt(2)), 3/(4sqrt(2)))

• (-3/(4sqrt(2)), 3/(4sqrt(2)))

• (-3/(4sqrt(2)), -3/(4sqrt(2)))

MCQ | Q 9

tan^-1(tan  (7pi)/6) = ______

• - pi/6

• pi/6

• (13pi)/6

• (5pi)/6

MCQ | Q 10

If sin(sin^-1(1/5) + cos^-1(x)) = 1, then x = ______

• 1/5

• -1/5

• 5

• −5

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 1 Trigonometric FunctionsVery Short Answers

#### 1 Mark

Very Short Answers | Q 1

Evaluate cot(tan−1(2x) + cot−1(2x))

Very Short Answers | Q 2

In ∆ABC, prove that ac cos B − bc cos A = a2 − b2

Very Short Answers | Q 3

In ∆ABC, if sin2A + sin2B = sin2C, then show that a2 + b2 = c2

Very Short Answers | Q 4

Find the polar co-ordinates of point whose Cartesian co-ordinates are (1 sqrt(3))

Very Short Answers | Q 5

Prove that 2 tan^-1 (3/4) = tan^-1(24/7)

Very Short Answers | Q 6

Evaluate sin[cos^-1 (3/5)]

Very Short Answers | Q 7

In ΔABC, a = 3, b = 4 and sin A = 3/4, find ∠B

Very Short Answers | Q 8

Find the principal solutions of cosec x = 2

Very Short Answers | Q 9

Find the principal solutions of sin x − 1 = 0

Very Short Answers | Q 10

Find the Cartesian co-ordinates of point whose polar co-ordinates are (4, pi/3)

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 1 Trigonometric FunctionsShort Answers I

#### 2 Marks each

Short Answers I | Q 1

With usual notations, prove that (cos "A")/"a" + (cos "B")/"b" + (cos "C")/"c" = ("a"^2 + "b"^2 + "c"^2)/(2"abc")

Short Answers I | Q 2

Find the principal solutions of cos 2𝑥 = 1

Short Answers I | Q 3

In ∆ABC, prove that ("b" - "c")^2 cos^2 ("A"/2) + ("b" + "c")^2 sin^2 ("A"/2) = a2

Short Answers I | Q 4

Find the principal solutions of sin x = -1/2

Short Answers I | Q 5

Find the value of cos^-1 (1/2) + tan^-1 (1/sqrt(3))

Short Answers I | Q 6

In ∆ABC, if a = 13, b = 14, c = 15, then find the value of cos B

Short Answers I | Q 7

In ∆ABC, if (cos "A")/"a" = (cos "B")/"b", then show that it is an isosceles triangle

Short Answers I | Q 8

Find the principal solutions of tan x = -sqrt(3)

Short Answers I | Q 9

Evaluate cos[pi/6 + cos^-1 (- sqrt(3)/2)]

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 1 Trigonometric FunctionsShort Answers II

#### 3 Marks

Short Answers II | Q 1

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

Short Answers II | Q 2

In ∆ABC, prove that (cos 2"A")/"a"^2 - (cos 2"c")/"c"^2 = 1/"a"^2 - 1/"c"^2

Short Answers II | Q 3

If tan−1x + tan−1y + tan−1z = π, then show that 1/(xy) + 1/(yz) + 1/(zx) = 1

Short Answers II | Q 4

Prove that sin [tan^-1 ((1 - x^2)/(2x)) + cos^-1 ((1 - x^2)/(1 + x^2))] = 1

Short Answers II | Q 5

In ∆ABC, if (2cos "A")/"a" + (cos "B")/"b" + (2cos"C")/"c" = "a"/"bc" + "b"/"ca", then show that the triangle is a right angled

Short Answers II | Q 6

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

Short Answers II | Q 7

If the angles A, B, C of ΔABC are in A.P. and its sides a, b, c are in G.P., then show that a2, b2, c2 are in A.P.

Short Answers II | Q 8

Prove that cot−1(7) + 2 cot−1(3) = pi/4

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 Chapter 1 Trigonometric FunctionsLong Answers III

#### 4 Marks

Long Answers III | Q 1

In ∆ABC, prove that (cos^2"A" - cos^2"B")/("a" + "b") + (cos^2"B" - cos^2"C")/("b" + "c") + (cos^2"C" - cos^2"A")/("c" + "a") = 0

Long Answers III | Q 2

Show that sin^-1(3/5)  + sin^-1(8/17) = cos^-1(36/85)

Long Answers III | Q 3

In ΔABC, prove that ("a"^2sin("B" - "C"))/(sin"A") + ("b"^2sin("C" - "A"))/(sin"B") + ("c"^2sin("A" - "B"))/(sin"C")

Long Answers III | Q 4

In ΔABC, prove that ("b"^2 - "c"^2)/"a" cos"A" + ("c"^2 - "a"^2)/"b" cos"B" + ("a"^2 - "b"^2)/"c" cos "C" = 0

Long Answers III | Q 5

Prove that 2 tan^-1 (1/8) + tan^-1 (1/7) + 2tan^-1 (1/5) = pi/4

Long Answers III | Q 6

In ∆ABC, if ∠A = pi/2, then prove that sin(B − C) = ("b"^2 - "c"^2)/("b"^2 + "c"^2)

Long Answers III | Q 7

If cos–1x + cos–1y – cos–1z = 0, then show that x2 + y2 + z2 – 2xyz = 1

## SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 1 - Trigonometric Functions

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Concepts covered in 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2021 chapter 1 Trigonometric Functions are Trigonometric Equations and Their Solutions, Solutions of Triangle, Inverse Trigonometric Functions.

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