The Principal value of ^(-1) ( -1/2 ) is: Option 1: ()/3 Option 2: (2)/3 Option 3: (5)/6 Option 4: (3)/4

Answer: (2)/3. Solution: Principal range of ^(-1) is [0, ]. ^(-1)(-x) = - ^(-1)(x). ^(-1)(-1/2) = - ()/3 = (2)/3.

Geometry

Trigonometry

Easy

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

$\frac{\pi}{3}$

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

$\frac{5\pi}{6}$

$\frac{3\pi}{4}$

✅ Correct Option: 2

Principal range of $\cos^{-1}$ is $[0, \pi]$ .

$\cos^{-1}(-x) = \pi - \cos^{-1}(x)$ .

$\cos^{-1}(-\frac{1}{2}) = \pi - \frac{\pi}{3} = \frac{2\pi}{3}$ .

2022: 30 Aug Shift 1

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

2025: 26 May Shift 2

Arrange the principal values of the following functions in ascending order

(A) $\cosec^{-1}(2)$

(B) $\tan^{-1}(-\sqrt{3})$

(D) $\tan^{-1}\left(\cos\frac{3\pi}{7}\right)$

Choose the correct answer from the options given below:

2022: 10 Aug Shift 1

Area of $\triangle ABD$ is

2025: 13 May Shift 2

Match List-I with List-II

Choose the correct answer from the options given below:

2023: 30 May Shift 3

The maximum value of $(\sin x)(\cos x)$ is :

2025: 3 June Shift 1

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