Which one of the following is TRUE? Option 1: ^(-1)1 1 Option 3: ^(-1)1 < 1 Option 4: ^(-1)1 < 1

Answer: ^(-1)1 1 0.64, ^(-1)1=0 1 0.84.

Geometry

Trigonometry

Medium

core

Which one of the following is TRUE?

$\cot^{-1}1 < \cot 1$

$\cos^{-1}1 > \cos 1$

$\sin^{-1}1 < \sin 1$

$\tan^{-1}1 < \tan 1$

✅ Correct Option: 4

Here $\tan^{-1}1=\frac{\pi}{4}\approx 0.79$ while $\tan 1\approx 1.56$ , so option 4 holds. The others fail: $\cot^{-1}1\approx 0.79>\cot 1\approx 0.64$ , $\cos^{-1}1=0<\cos 1\approx 0.54$ , and $\sin^{-1}1\approx 1.57>\sin 1\approx 0.84$ .

2022: 30 Aug Shift 1

$\sin^{-1}(1 - x) - 2\sin^{-1}x = \frac{\pi}{2}$ , than $x$ is equal to

(a) $0$

(b) $1$

(d) $2$

Choose the most appropriate answer from the options given below:

2022: 30 Aug Shift 1

The value of $\sin\left[2\cot^{-1}\left(\frac{-5}{12}\right)\right]$ is :

2022: 23 Aug Shift 1

$\sin^{-1}(\cos x) = \frac{\pi}{2} - x$ is valid for :

2026: 18 May Shift 2

Match the LIST-I with LIST-II

LIST-I Functions	LIST-II Principal value
A. $\sin^{-1}\left(\dfrac{1}{2}\right)$	I. $\dfrac{\pi}{4}$
B. $\sin^{-1}\left(-\dfrac{1}{\sqrt{2}}\right)$	II. $\dfrac{\pi}{6}$
C. $\tan^{-1}(1)$	III. $-\dfrac{\pi}{4}$
D. $\cos^{-1}\left(-\dfrac{1}{2}\right)$	IV. $\dfrac{2\pi}{3}$

Choose the correct answer from the options given below:

2025: 3 June Shift 1

The value of $-\cosec^2(\cot^{-1}y) + \sec^2( \tan^{-1}x)$ is equal to

2022: 4 Aug Shift 1

Match List - I with List - II

List - I	List - II
A. $\tan^{-1}\left(\tan\frac{7\pi}{6}\right)$	I. $\frac{5\pi}{6}$
B. $\tan^{-1}\left(\tan\frac{8\pi}{6}\right)$	II. $\frac{\pi}{2}$
C. $\tan^{-1}\frac{1}{\sqrt{3}} + cosec^{-1}\frac{2}{\sqrt{3}}$	III. $\frac{\pi}{6}$
D. $\cos^{-1}\left(\cos\frac{5\pi}{6}\right)$	IV. $\frac{\pi}{3}$

Choose the correct answer from the options given below:

Which one of the following is TRUE?

Solution

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