Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 5 - Inverse Trigonometric Functions>DPP>Q 9

MEDIUM

JEE Main

IMPORTANT

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$x, y, z \in R$ are such that they satisfy $x + y + z = 1$ and $\tan^{- 1} x + \tan^{- 1} y + \tan^{- 1} z = \frac{π}{4},$ then the value of $|x^{3} + y^{3} + z^{3} - 3|$ is

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Important Questions on Inverse Trigonometric Functions

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 5 - Inverse Trigonometric Functions>DPP>Q 10

The complete set of values of

a

for which the function

f (x) = \tan^{- 1} (x^{2} - 18 x + a) > 0; \forall x \in R

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 5 - Inverse Trigonometric Functions>DPP>Q 11

The value of

\cos^{- 1} (- \sin \frac{7 π}{6})

is

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 5 - Inverse Trigonometric Functions>DPP>Q 12

The value of

\sec [\sin^{- 1} (- \sin \frac{50 π}{9}) + \cos^{- 1} (\cos (- \frac{31 π}{9}))]

is equal to

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 5 - Inverse Trigonometric Functions>DPP>Q 13

The maximum value of the function

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

HARD

JEE Main

IMPORTANT

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

The solution of the equation

\sin^{- 1} |\sin x| = \sqrt{\sin^{- 1} |\sin x|}

is

HARD

JEE Main

IMPORTANT

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

The value of

\sin (\frac{1}{4} \sin^{- 1} \frac{\sqrt{63}}{8})

is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 5 - Inverse Trigonometric Functions>DPP>Q 16

Let

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

, then which of the following statement is/are true?

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Trigonometry JEE Main & Advanced>Chapter 5 - Inverse Trigonometric Functions>DPP>Q 17

If

f (x) = \sin^{- 1} (\sin x), g (x) = \cos^{- 1} (\cos x)

and

h (x) = \cot^{- 1} (\cot x),

then which of the following is/are correct?