Let f ( x ) = cos 2 tan - 1 sin cot - 1 1 - x x , 0 < x < 1 . Then:

( 1 - x ) 2 f ' ( x ) + 2 ( f ( x ) ) 2 = 0

( 1 + x ) 2 f ' ( x ) + 2 ( f ( x ) ) 2 = 0

( 1 - x ) 2 f ' ( x ) - 2 ( f ( x ) ) 2 = 0

( 1 + x ) 2 f ' ( x ) - 2 ( f ( x ) ) 2 = 0

HARD

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If $t a n^{- 1} \frac{1}{2 x + 1} + t a n^{- 1} \frac{1}{4 x + 1} = c o t^{- 1} (\frac{x^{2}}{2})$ , then the number of all possible values of $x$ is/are

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Important Questions on Inverse Trigonometric Functions

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Inverse Trigonometric Equations and Inequalities

\cot^{- 1} (α) = \cot^{- 1} 2 + \cot^{- 1} 8 + \cot^{- 1} 18 + \cot^{- 1} 32 + \dots .

upto

100

terms, then

α

is:

HARD

Mathematics>Trigonometry>Inverse Trigonometric Functions>Inverse Trigonometric Equations and Inequalities

\cos^{- 1} \sqrt{p} + \cos^{- 1} \sqrt{1 - p} + \cos^{- 1} \sqrt{1 - q} = \frac{3 π}{4},

then the value of

q

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Inverse Trigonometric Equations and Inequalities

\sin^{- 1} (\frac{x}{5}) + \cos^{- 1} (\frac{4}{5}) = \frac{π}{2},

then the value of

x

is equal to

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Inverse Trigonometric Equations and Inequalities

\cot (\sin^{- 1} x) = \cos (\tan^{- 1} \sqrt{3}),

then

x =

HARD

Mathematics>Trigonometry>Inverse Trigonometric Functions>Inverse Trigonometric Equations and Inequalities

The value of

10 \tan (\cot^{- 1} 3 + \cot^{- 1} 7)

equal to

MEDIUM

Mathematics>Trigonometry>Inverse Trigonometric Functions>Inverse Trigonometric Equations and Inequalities

The number of real roots of the equation

\tan^{- 1} \sqrt{x (x + 1)} + \sin^{- 1} \sqrt{x^{2} + x + 1} = \frac{π}{4}

is:

MEDIUM

Mathematics>Trigonometry>Inverse Trigonometric Functions>Inverse Trigonometric Equations and Inequalities

\cot^{- 1} (\sqrt{\cos α}) - \tan^{- 1} (\sqrt{\cos α}) = x,

then

\sin x

is equal to

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Inverse Trigonometric Equations and Inequalities

\sin^{- 1} x - \cos^{- 1} x = \frac{π}{6}

, then

x

MEDIUM

Mathematics>Trigonometry>Inverse Trigonometric Functions>Inverse Trigonometric Equations and Inequalities

The value of

\cos (\cos^{- 1} \frac{1}{5} + 2 \sin^{- 1} \frac{1}{5})

is equal to

MEDIUM

Mathematics>Trigonometry>Inverse Trigonometric Functions>Inverse Trigonometric Equations and Inequalities

\sin^{- 1} x + \tan^{- 1} x = π / 2

, then

2 x^{2} + 1 =

HARD

Mathematics>Trigonometry>Inverse Trigonometric Functions>Inverse Trigonometric Equations and Inequalities

A value of

x

satisfying the equation

\sin [\cot^{- 1} (1 + x)] = \cos [\tan^{- 1} x],

is:

MEDIUM

Mathematics>Trigonometry>Inverse Trigonometric Functions>Inverse Trigonometric Equations and Inequalities

\cos^{- 1} x - \cos^{- 1} \frac{y}{2} = α,

where

- 1 \leq x \leq 1, - 2 \leq y \leq 2, x \leq \frac{y}{2},

then for all

x, y, 4 x^{2} - 4 x y \cos α + y^{2}

is equal to :

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Inverse Trigonometric Equations and Inequalities

What is the value of

' x',

3 \tan^{- 1} {1 / (2 + \sqrt{3})} \tan^{- 1} x = \tan^{- 1} (1 / 3) ?

HARD

Mathematics>Trigonometry>Inverse Trigonometric Functions>Inverse Trigonometric Equations and Inequalities

Which of the following values of

x

does not satisfy the equation

\sin (2 \cos^{- 1} (\cot (2 \tan^{- 1} x))) = 0

MEDIUM

Mathematics>Trigonometry>Inverse Trigonometric Functions>Inverse Trigonometric Equations and Inequalities

Let

f (x) = \cos (2 \tan^{- 1} \sin (\cot^{- 1} \sqrt{\frac{1 - x}{x}})), 0 < x < 1

. Then:

MEDIUM

Mathematics>Trigonometry>Inverse Trigonometric Functions>Inverse Trigonometric Equations and Inequalities

Value of

\sin^{- 1} \frac{3}{5} - \sin^{- 1} \frac{8}{17}

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Inverse Trigonometric Equations and Inequalities

\cos^{- 1} (\frac{5}{13}) - \sin^{- 1} (\frac{12}{13}) = \cos^{- 1} x

, then

x

is equal to

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Inverse Trigonometric Equations and Inequalities

\tan^{- 1} (\frac{1 - x}{1 + x}) - \frac{1}{2} \tan^{- 1} x = 0,

for

x > 0,

then

x =

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Inverse Trigonometric Equations and Inequalities

4 {s i n}^{- 1} x + 6 {c o s}^{- 1} x = 3 π,

then

x =

MEDIUM

Mathematics>Trigonometry>Inverse Trigonometric Functions>Inverse Trigonometric Equations and Inequalities

The value of

\tan^{- 1} [\frac{\sqrt{1 + x^{2}} + \sqrt{1 - x^{2}}}{\sqrt{1 + x^{2}} - \sqrt{1 - x^{2}}}],

|x| < \frac{1}{2}, x \neq 0,

is equal to:

If tan-112x+1+tan-114x+1=cot-1x22, then the number of all possible values of x is/are

Important Questions on Inverse Trigonometric Functions

Learn and Prepare for any exam you want !

If $t a n^{- 1} \frac{1}{2 x + 1} + t a n^{- 1} \frac{1}{4 x + 1} = c o t^{- 1} (\frac{x^{2}}{2})$ , then the number of all possible values of $x$ is/are