The simplest form of ^(-1)\x/(√(a^2 - x^2))\ is, where -a < x < a. Option 1: ^(-1)x/a Option 2: ^(-1)(ax) Option 3: a ^(-1)x/a Option 4: ^(-1)x/a

Answer: ^(-1)x/a. Solution: Let x = a. Then √(a^2 - x^2) = a. The given expression becomes ^(-1)(a/(a)) = ^(-1)() = = ^(-1)(x/a).

Geometry

Trigonometry

Medium

core

The simplest form of $\tan^{-1}\left\{\frac{x}{\sqrt{a^2 - x^2}}\right\}$ is, where $-a < x < a$ .

$\tan^{-1}\frac{x}{a}$

$\tan^{-1}(ax)$

$a \tan^{-1}\frac{x}{a}$

$\sin^{-1}\frac{x}{a}$

✅ Correct Option: 4

Let $x = a\sin\theta$ . Then $\sqrt{a^2 - x^2} = a\cos\theta$ . The given expression becomes $\tan^{-1}(a\sin\theta/(a\cos\theta)) = \tan^{-1}(\tan\theta) = \theta = \sin^{-1}(x/a)$ .

2026: 22 May Shift 1

Match List-I with List-II

List-I (Function)	List-II (Principal value of y)
(A) $y=\sin^{-1}\left(-\frac{1}{2}\right)$	(I) $\frac{3\pi}{4}$
(B) $y=\cot^{-1}\left(-\frac{1}{\sqrt3}\right)$	(II) $-\frac{\pi}{4}$
(C) $y=cosec^{-1}(-\sqrt2)$	(III) $-\frac{\pi}{6}$
(D) $y=\cos^{-1}\left(-\frac{1}{\sqrt2}\right)$	(IV) $\frac{2\pi}{3}$

Choose the correct answer from the options given below:

2025: 16 May Shift 1

Match List-I with List-II

List-I	List-II
Inverse Trigonometric function	Principal values of arguments
(A) $sin^{-1}\left(\frac{-1}{2}\right)$	(I) $\frac{-\pi}{3}$
(B) $cos^{-1}\left(\frac{-1}{2}\right)$	(II) $\frac{3\pi}{4}$
(C) $tan^{-1}(-\sqrt{3})$	(III) $\frac{-\pi}{6}$
(D) $sec^{-1}(-\sqrt{2})$	(IV) $\frac{2\pi}{3}$

Choose the correct answer from the options given below:

2025: 14 May Shift 1

for $|x| < 1$ , $sin (tan^{-1}x)$ equal to

2026: 14 May Shift 2

Match the LIST-I with LIST-II

	LIST-I (Functions)		LIST-II (Principal Values)
A.	$\sin^{-1}\left(-\dfrac{1}{2}\right) + \cos^{-1}\left(-\dfrac{1}{2}\right)$	I.	$-\dfrac{\pi}{3}$
B.	$\cos^{-1}\left(\dfrac{1}{2}\right) + 2\sin^{-1}\left(\dfrac{1}{2}\right)$	II.	$\dfrac{3\pi}{4}$
C.	$\tan^{-1}\sqrt{3} - \sec^{-1}(-2)$	III.	$\dfrac{\pi}{2}$
D.	$\cos^{-1}\left(-\dfrac{1}{\sqrt{2}}\right)$	IV.	$\dfrac{2\pi}{3}$

Choose the correct answer from the options given below:

2026: 29 May Shift 1

The value of $\tan^{-1}(\sqrt3)-\sec^{-1}(-2)$ is

2025: 3 June Shift 2

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

The simplest form of tan⁡−1{xa2−x2}\tan^{-1}\left\{\frac{x}{\sqrt{a^2 - x^2}}\right\}tan−1{a2−x2​x​} is, where −a<x<a-a < x < a−a<x<a.

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The simplest form of $\tan^{-1}\left\{\frac{x}{\sqrt{a^2 - x^2}}\right\}$ is, where $-a < x < a$ .