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

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 25 June 2022 Shift 2>Q 36

The value of

\tan^{- 1} [\frac{\cos (\frac{15 π}{4}) - 1}{\sin (\frac{π}{4})}]

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 26 June 2022 Shift 2>Q 37

If the inverse trigonometric functions take principal values, then

\cos^{- 1} (\frac{3}{10} \cos (\tan^{- 1} (\frac{4}{3})) + \frac{2}{5} \sin (\tan^{- 1} (\frac{4}{3})))

is equal to

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 July 2022 Shift 2>Q 42

Let

x = \sin (2 \tan^{- 1} α)

and

y = \sin (\frac{1}{2} \tan^{- 1} \frac{4}{3})

. If

S = \{α \in ℝ : y^{2} = 1 - x\}

, then

\sum_{α \in S} 16 α^{3}

is equal to _______.