Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 4 - Inverse Trigonometric Functions>Target Exercises>Q 65

HARD

JEE Advanced

IMPORTANT

Earn 100

The number of the real solution of $\sqrt{1 + \cos 2 x} = \sqrt{2} \sin^{- 1} (\sin x), - π \leq x \leq π$ is

50% studentsanswered this correctly

Important Questions on Inverse Trigonometric Functions

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 4 - Inverse Trigonometric Functions>Target Exercises>Q 66

The number of real solutions of the equation

\tan^{- 1} \sqrt{x (x + 1)} + \sin^{- 1} \sqrt{x^{2} + x + 1} = \frac{π}{2}

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 4 - Inverse Trigonometric Functions>Target Exercises>Q 67

The number of real solutions

(x, y)

where

|y| = \sin x, y = \cos^{- 1} (\cos x), - 2 π \leq x \leq 2 π

, is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 4 - Inverse Trigonometric Functions>Target Exercises>Q 68

The set of values of

k

for which

x^{2} - k x + \sin^{- 1} (\sin 4) > 0

for all real

x

, is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 4 - Inverse Trigonometric Functions>Target Exercises>Q 69

The sum of the infinite series

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

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 4 - Inverse Trigonometric Functions>Target Exercises>Q 70

If $x_{1}, x_{2}, x_{3}$ and $x_{4}$ are roots of the equation $x^{4} - x^{3} \sin 2 β + x^{2} \cos 2 β - x \cos β - \sin β = 0$ , then $\sum_{i = 1}^{4} \tan^{- 1} x_{i}$ is equal to

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 4 - Inverse Trigonometric Functions>Target Exercises>Q 71

If

\sum_{i = 1}^{2 n} \cos^{- 1} x_{i} = 0

, then

\sum_{i = 1}^{2 n} x_{i}

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 4 - Inverse Trigonometric Functions>Target Exercises>Q 72

If

\sum_{i = 1}^{20} \sin^{- 1} x_{i} = 10 π

, then

\sum_{i = 1}^{20} x_{i}

is equal to