Geometry

Trigonometry

Hard

core

Match the LIST-I with LIST-II

LIST-I Function LIST-II Value
A. $\tan[\cos^{-1}(\sin(\tan^{-1} 4/3))]$ I. $1/\sqrt2$
B. $\sin\left(2\tan^{-1}\left(\dfrac{3}{4}\right)\right)$ II. 1
C. $\cos\left[\tan^{-1}\left(\dfrac{1}{2}\right)+\tan^{-1}\left(\dfrac{1}{3}\right)\right]$ III. 24/25
D. $\sin\left[\dfrac{\pi}{3} - \sin^{-1}(-1/2)\right]$ IV. 3/4

Choose the correct answer from the options given below:

LIST-I Function	LIST-II Value
A. $\tan[\cos^{-1}(\sin(\tan^{-1} 4/3))]$	I. $1/\sqrt2$
B. $\sin\left(2\tan^{-1}\left(\dfrac{3}{4}\right)\right)$	II. 1
C. $\cos\left[\tan^{-1}\left(\dfrac{1}{2}\right)+\tan^{-1}\left(\dfrac{1}{3}\right)\right]$	III. 24/25
D. $\sin\left[\dfrac{\pi}{3} - \sin^{-1}(-1/2)\right]$	IV. 3/4

A-I, B-II, C-IV, D-III

A-IV, B-III, C-II, D-I

A-II, B-I, C-III, D-IV

A-IV, B-III, C-I, D-II

✅ Correct Option: 4

A: $\sin(\tan^{-1}\frac43)=\frac45$ , then $\tan(\cos^{-1}\frac45)=\frac34$ (IV).

B: $\sin 2\theta=\dfrac{2t}{1+t^2}$ with $t=\frac34$ gives $\frac{24}{25}$ (III).

C: $\tan^{-1}\frac12+\tan^{-1}\frac13=\frac{\pi}{4}$ , cosine $=\frac{1}{\sqrt2}$ (I).

D: $\sin(\frac{\pi}{3}+\frac{\pi}{6})=\sin\frac{\pi}{2}=1$ (II).

2026: 12 May Shift 2

Match List-I with List-II

List-I (Functions)	List-II (Range, principal value)
(A) $\sin^{-1}x$	(I) $[0,\pi]-\left\{\dfrac{\pi}{2}\right\}$
(B) $\tan^{-1}x$	(II) $\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right]-\{0\}$
(C) $cosec^{-1}x$	(III) $\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right]$
(D) $\sec^{-1}x$	(IV) $\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right)$

Choose the correct answer from the options given below:

2023: 22 May Shift 3

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

2023: 23 May Shift 3

The maximum value of $\sin x + \cos x, x \in R$ is:

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:

2026: 30 May Shift 2

Match List-I with List-II

Choose the correct answer from the options given below:

2022: 6 Aug Shift 2

The Principal value of $\cos^{-1} \left( -\frac{1}{2} \right)$ is:

Solution