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

HARD

JEE Main

IMPORTANT

Earn 100

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 _____ .

69.23% studentsanswered this correctly

Important Questions on Inverse Trigonometric Functions

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

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 31 January 2023 Shift 2>Q 53

Let

(a, b) \subset (0, 2 π)

be the largest interval for which

\sin^{- 1} (\sin θ) - \cos^{- 1} (\sin θ) > 0, θ \in (0, 2 π)

, holds . If

α x^{2} + β x + \sin^{- 1} (x^{2} - 6 x + 10) + \cos^{- 1} (x^{2} - 6 x + 10) = 0

and

α - β = b - a

, then

α

is equal to;

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 1 February 2023 Shift 1>Q 54

Let

S

be the set of all solutions of the equation

\cos^{- 1} (2 x) - 2 \cos^{- 1} (\sqrt{1 - x^{2}}) = π, x \in [- \frac{1}{2}, \frac{1}{2}]

. Then

\sum_{x \in S} 2 \sin^{- 1} (x^{2} - 1)

is equal to

EASY

JEE Main

IMPORTANT

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

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 :