The principal value of ^(-1)((-1)/√3) is : Option 1: -(2)/3 Option 2: (2)/3 Option 3: ()/3 Option 4: -()/3

Answer: (2)/3. Solution: Range of ^(-1) is (0,). =-1/√3 means =-√3. In (0,), this occurs at =(2)/3.

Geometry

Trigonometry

Easy

core

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

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

$\frac{2\pi}{3}$

$\frac{\pi}{3}$

$-\frac{\pi}{3}$

✅ Correct Option: 2

Range of $\cot^{-1}$ is $(0,\pi)$ .

$\cot\theta=-\frac{1}{\sqrt{3}}$ means $\tan\theta=-\sqrt{3}$ .

In $(0,\pi)$ , this occurs at $\theta=\frac{2\pi}{3}$ .

2022: 23 Aug Shift 1

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

2025: 13 May Shift 2

Match List-I with List-II

Choose the correct answer from the options given below:

2023: 23 May Shift 3

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

2022: 4 Aug Shift 1

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

2026: 29 May Shift 1

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

2025: 14 May Shift 1

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