EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 24 June 2022 Shift 1>Q 34

HARD

JEE Main

IMPORTANT

Earn 100

The set of all values of $k$ for which ${(\tan^{- 1} x)}^{3} + {(\cot^{- 1} x)}^{3} = k π^{3}, x \in R$ , is the interval

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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 - 24 June 2022 Shift 2>Q 35

If

y = \tan^{- 1} (\sec x^{3} - \tan x^{3}), \frac{π}{2} < x^{3} < \frac{3 π}{2}

, then

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 27 June 2022 Shift 1>Q 38

\sin^{- 1} (\sin \frac{2 π}{3}) + \cos^{- 1} (\cos \frac{7 π}{6}) + \tan^{- 1} (\tan \frac{3 π}{4})

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 27 June 2022 Shift 2>Q 39

The value of

\cot (\sum_{n = 1}^{50} \tan^{- 1} (\frac{1}{1 + n + n^{2}}))

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 28 June 2022 Shift 2>Q 40

The value of

\lim_{n \to \infty} 6 \tan \{\sum_{r = 1}^{n} \tan^{- 1} (\frac{1}{r^{2} + 3 r + 3})\}

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 29 June 2022 Shift 1>Q 41

50 \tan (3 \tan^{- 1} (\frac{1}{2}) + 2 \cos^{- 1} (\frac{1}{\sqrt{5}})) +

4 \sqrt{2} \tan (\frac{1}{2} \tan^{- 1} (2 \sqrt{2}))

is equal to ______.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 25 January 2023 Shift 1>Q 50

If the sum of all the solutions of

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

,

- 1 < x < 1, x \neq 0

, is

α - \frac{4}{\sqrt{3}}

, then

α

is equal to _____ .

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 30 January 2023 Shift 2>Q 51

Let

a_{1} = 1, a_{2}, a_{3}, a_{4}, \dots .

. be consecutive natural numbers. Then

\tan^{- 1} (\frac{1}{1 + a_{1} a_{2}}) + \tan^{- 1} (\frac{1}{1 + a_{2} a_{3}})

+ \dots . . + \tan^{- 1} (\frac{1}{1 + a_{2021} a_{2022}})

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 31 January 2023 Shift 1>Q 52

If

\sin^{- 1} \frac{α}{17} + \cos^{- 1} \frac{4}{5} - \tan^{- 1} \frac{77}{36} = 0, 0 < α < 13

, then

\sin^{- 1} (\sin α) + \cos^{- 1} (\cos α)

is equal to