हिंदी

Show that tan-1 12-tan-1 14=tan-1 29. - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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

योग
Advertisements

उत्तर

LHS = `tan^-1  1/2 - tan^-1  1/4`

`= tan^-1 [(1/2 - 1/4)/(1 + (1/2)(1/4))]`

`= tan^-1 ((4 - 2)/(8 + 1))`

`= tan^-1 (2/9)` = RHS.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Trigonometric Functions - Miscellaneous exercise 3 [पृष्ठ ११०]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
अध्याय 3 Trigonometric Functions
Miscellaneous exercise 3 | Q 30 | पृष्ठ ११०

संबंधित प्रश्न

Find the principal solution of the following equation:

cot θ = 0


Find the general solution of the following equation:

tan θ = `(1)/(sqrt(3))`


Find the general solution of the following equation:

cosec θ = - √2.


Find the general solution of the following equation:

tan θ = - 1


Find the general solution of the following equation:

cot 4θ = – 1


Find the general solution of the following equation:

sin θ = tan θ


Find the general solution of the following equation: 

tan3θ = 3 tanθ.


Find the general solution of the following equation:

cosθ + sinθ = 1.


State whether the following equation have solution or not?

3 tanθ = 5


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


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


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


Select the correct option from the given alternatives:

The general solution of sec x = `sqrt(2)` is ______.


Select the correct option from the given alternatives:

If cos pθ = cos qθ, p ≠ q, then ______.


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


The principal value of sin1 `(- sqrt3/2)` is ______.


Select the correct option from the given alternatives:

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


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


Find the principal solutions of the following equation:

tan 3θ = - 1


Find the general solutions of the following equation:

sin θ - cos θ = 1


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


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


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


Show that `2 cot^(-1)  3/2 +  sec^(-1)  13/12 = π/2`


Prove the following:

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


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


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


If sin-1 x = `pi/10`, for some x ∈ [-1, 1], then the value of cos-1 x is _______.


The value of tan 57°- tan 12°- tan 57° tan 12° is ______.


If y = sin-1 `[(sqrt(1 + x) + sqrt(1 - x))/2]`, then `"dy"/"dx"` = ?


The principal solutions of cot x = `sqrt3` are ______.


If 2 cos2 θ + 3 cos θ = 2, then permissible value of cos θ is ________.


The values of x in `(0, pi/2)` satisfying the equation sin x cos x = `1/4` are ______.


The number of solutions of `sin^2 theta = 1/2` in [0, π] is ______.


The value of sin 18° is ______.


The measure of the angle between lines (sin2θ - 1)x2 - 2xy cos2θ + cos2θy2 = 0 is ______ 


The general solution of sin 2x = cos 2x is ______ 


If sin θ + cos θ = 1, then the general value of θ is ______.


If `(tan 3 theta - 1)/(tan 3 theta + 1) = sqrt3`, then the general value of θ is ______.


The general solution of cosec x = `-sqrt2` is ______ 


If a = sin θ + cos θ, b = sin3 θ + cos3 θ, then ______.


The general solution to cos100x – sin100x = 1 is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×