EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 1 September 2021 Shift 2>Q 6

EASY

JEE Main

IMPORTANT

Earn 100

$\cos^{- 1} (\cos (- 5)) + \sin^{- 1} (\sin (6)) - \tan^{- 1} (\tan (12))$ is equal to

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Important Questions on Inverse Trigonometric Functions

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 20 July 2021 Shift 1>Q 7

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

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 20 July 2021 Shift 2>Q 8

The value of

\tan (2 \tan^{- 1} (\frac{3}{5}) + \sin^{- 1} (\frac{5}{13}))

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main 16 March 2021 Shift 2>Q 9

Given that the inverse trigonometric functions take principal values only. Then, the number of real values of $x$ which satisfy $\sin^{- 1} (\frac{3 x}{5}) + \sin^{- 1} (\frac{4 x}{5}) = \sin^{- 1} x$ is equal to:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main 17 March 2021 Shift 1>Q 10

If

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

upto

100

terms, then

α

is:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main 17 March 2021 Shift 1>Q 11

The sum of possible values of

x

for

\tan^{- 1} (x + 1) + \cot^{- 1} (\frac{1}{x - 1}) = \tan^{- 1} (\frac{8}{31})

is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main 17 March 2021 Shift 1>Q 12

If

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

and its first derivative with respect to

x

is

- \frac{b}{a} \log_{e} 2

when

x = 1,

where

a

and

b

are integers, then the minimum value of

|a^{2} - b^{2}|

is _______.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main 17 March 2021 Shift 2>Q 13

The number of solutions of the equation

\sin^{- 1} [x^{2} + \frac{1}{3}] + \cos^{- 1} [x^{2} - \frac{2}{3}] = x^{2}

for

x \in [- 1, 1]

, and

[x]

denotes the greatest integer less than or equal to

x,

is :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 24 Feb 2021 Shift 1>Q 14

\lim_{n \to \infty} \tan \{\sum_{r = 1}^{n} \tan^{- 1} (\frac{1}{1 + r + r^{2}})\}

is equal to_______.