For x [-1,1], if 4^-1x + ^-1x = then x is equal to Option 1: -1/2 Option 2: 1/2 Option 3: sqrt(3)2 Option 4: -sqrt(3)2

The answer is '1/2'. View full solution:

Geometry > Trigonometry

Medium

core

For $x \in [-1,1]$, if $4\sin^{-1}x + \cos^{-1}x = \pi$ then $x$ is equal to

$-\frac{1}{2}$

$\frac{1}{2}$

$\frac{\sqrt{3}}{2}$

$\frac{-\sqrt{3}}{2}$

✅ Correct Option: 2

Related questions:

2022: 17 Aug Shift 2

Match List - I with List - II.

List - I	List - II
(A) $\tan^{-1}\sqrt{3} - \sec^{-1}(-2)$	(I) $\frac{3\pi}{4}$
(B) $\cot^{-1}\left(\frac{-1}{\sqrt{3}}\right)$	(II) $-\frac{\pi}{3}$
(C) $\cos^{-1}\left(-\frac{1}{\sqrt{2}}\right)$	(III) $\frac{\pi}{2}$
(D) $\cos^{-1}\left(\frac{1}{2}\right) + \sin^{-1}\left(\frac{1}{2}\right)$	(IV) $\frac{2\pi}{3}$

Choose the correct answer from the options given below :

2026: 30th May Shift 1

The value of $2\sec^2(\tan^{-1}2)+3\text{cosec}^2(\cot^{-1}3)$ is:

2023: 22 May Shift 3

The principal value of $\cot^{-1}\left(\frac{-1}{\sqrt{3}}\right)$ is :

2022: 10 Aug Shift 1

Area of $\triangle ABD$ is

2025: 3 June Shift 2

The value of $\tan^{-1}(2) + \tan^{-1}(3)$ is equal to

2023: 15 June Shift 2

Match List - I with List - II.

Choose the correct answer from the options given below :