NCERT Solutions
Class 12 - Mathematics Part-1 - Chapter 2: INVERSE TRIGONOMETRIC FUNCTIONS

EXERCISE 2.1

Find the principal value of \( \sin^{-1}\left(-\dfrac{1}{2}\right) \).

Find the principal value of \( \cos^{-1}\left(\dfrac{\sqrt{3}}{2}\right) \).

Find the principal value of \( \text{cosec}^{-1}(2) \).

Find the principal value of \( \tan^{-1}(-\sqrt{3}) \).

Find the principal value of \( \cos^{-1}\left(-\dfrac{1}{2}\right) \).

Find the principal value of \( \tan^{-1}(-1) \).

Find the principal value of \( \sec^{-1}\left(\dfrac{2}{\sqrt{3}}\right) \).

Find the principal value of \( \cot^{-1}(\sqrt{3}) \).

Find the principal value of \( \cos^{-1}\left(-\dfrac{1}{\sqrt{2}}\right) \).

Find the principal value of \( \text{cosec}^{-1}(-\sqrt{2}) \).

Find the value of \( \tan^{-1}(1) + \cos^{-1}\left(-\dfrac{1}{2}\right) + \sin^{-1}\left(-\dfrac{1}{2}\right) \).

Find the value of \( \cos^{-1}\left(\dfrac{1}{2}\right) + 2\sin^{-1}\left(\dfrac{1}{2}\right) \).

If \( \sin^{-1} x = y \), then which of the following is correct?

(A) \( 0 \le y \le \pi \)

(B) \( -\dfrac{\pi}{2} \le y \le \dfrac{\pi}{2} \)

(C) \( 0 < y < \pi \)

(D) \( -\dfrac{\pi}{2} < y < \dfrac{\pi}{2} \)

Find the value of \( \tan^{-1}(\sqrt{3}) - \sec^{-1}(-2) \).

(A) \( \pi \)

(B) \( -\dfrac{\pi}{3} \)

(C) \( \dfrac{\pi}{3} \)

(D) \( \dfrac{2\pi}{3} \)