Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 5 - Inverse Trigonometric Functions>DPP>Q 14

HARD

JEE Main

IMPORTANT

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If $\sin^{- 1} (\frac{\sqrt{x}}{2}) + \sin^{- 1} (\sqrt{1 - \frac{x}{4}}) + \tan^{- 1} y = \frac{2 π}{3}$ , then

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Important Questions on Inverse Trigonometric Functions

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 5 - Inverse Trigonometric Functions>DPP>Q 15

\cos^{- 1} (\sqrt{\frac{a - x}{a - b}}) = \sin^{- 1} (\sqrt{\frac{x - b}{a - b}})

is possible if

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 5 - Inverse Trigonometric Functions>DPP>Q 1

The sum of the roots of the equation $\tan^{- 1} (x + 3) - \tan^{- 1} (x - 3) = \sin^{- 1} \frac{3}{5}$ is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 5 - Inverse Trigonometric Functions>DPP>Q 2

If

x

and

y

are positive integers satisfying

\tan^{- 1} (\frac{1}{x}) + \tan^{- 1} (\frac{1}{y}) = \tan^{- 1} (\frac{1}{7}),

then the number of ordered pairs of

(x, y)

is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 5 - Inverse Trigonometric Functions>DPP>Q 3

Number of roots of equation

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

is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 5 - Inverse Trigonometric Functions>DPP>Q 4

If

x > 1

and

\cos^{- 1} (\frac{x^{2} - 1}{x^{2} + 1}) + \tan^{- 1} (\frac{2 x}{x^{2} - 1}) = \frac{2 π}{3},

then

x

=

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 5 - Inverse Trigonometric Functions>DPP>Q 5

The solution of

\sin^{- 1} x - \sin^{- 1} 2 x = \pm \frac{π}{3}

is

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 5 - Inverse Trigonometric Functions>DPP>Q 6

If

\cos^{- 1} (\frac{1 - x^{2}}{1 + x^{2}}) + \sin^{- 1} (\frac{2 x}{1 + x^{2}}) = p

for all

x \in [- 1, 0],

then

p

is equal to

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 5 - Inverse Trigonometric Functions>DPP>Q 7

Let

f (x) = \sin^{- 1} (\frac{2 x}{1 + x^{2}})

and

g (x) = \cos^{- 1} (\frac{x^{2} - 1}{x^{2} + 1}) .

Then the value of

f (10) - g (100)

is equal to