EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 1 February 2023 Shift 2>Q 55

EASY

JEE Main

IMPORTANT

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Let $S = \{x \in R : 0 < x < 1 and 2 \tan^{- 1} (\frac{1 - x}{1 + x}) = \cos^{- 1} (\frac{1 - x^{2}}{1 + x^{2}})\}$ . If $n (S)$ denotes the number of elements in $S$ then :

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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 - 26 August 2021 Shift 1>Q 1

Let

f (x) = \cos (2 \tan^{- 1} \sin (\cot^{- 1} \sqrt{\frac{1 - x}{x}})), 0 < x < 1

. Then:

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 26 August 2021 Shift 2>Q 2

If

\sum_{r = 1}^{50} \tan^{- 1} \frac{1}{2 r^{2}} = p,

then the value of

\tan p

is :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 27 August 2021 Shift 1>Q 3

If

{(\sin^{- 1} x)}^{2} - {(\cos^{- 1} x)}^{2} = a; 0 < x < 1, a \neq 0,

then the value of

2 x^{2} - 1

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 27 August 2021 Shift 2>Q 4

If

y (x) = \cot^{- 1} (\frac{\sqrt{1 + \sin x} + \sqrt{1 - \sin x}}{\sqrt{1 + \sin x} - \sqrt{1 - \sin x}}), x \in (\frac{π}{2}, π)

, then

\frac{d y}{d x}

at

x = \frac{5 π}{6}

is:

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 31 August 2021 Shift 2>Q 5

The domain of the function,

f (x) = \sin^{- 1} (\frac{3 x^{2} + x - 1}{(x - 1)^{2}}) + \cos^{- 1} (\frac{x - 1}{x + 1})

is:

EASY

JEE Main

IMPORTANT

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

\cos^{- 1} (\cos (- 5)) + \sin^{- 1} (\sin (6)) - \tan^{- 1} (\tan (12))

is equal to

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: