List of top Mathematics Questions on Inverse Trigonometric Functions

Find the principal value of \( \sin^{-1}\!\left(-\frac{\sqrt{3}}{2}\right) + \cosec^{-1}\left(-\frac{2}{\sqrt{3}}\right). \)\!
\( \frac{d}{dx} \left( \sin x^2 \right) = 2x \cos x^2 \)
The principal value of \( \tan^{-1}(\sqrt{3}) \) is:
If \( \sin^{-1}x + \cos^{-1}x = \frac{\pi}{2} \), then \( x \) is:
Prove that \[ 2 \tan^{-1} \left( \frac{1}{3} \right) + \tan^{-1} \left( \frac{1}{7} \right) = \frac{\pi}{4} \]
\( \tan^{-1} \sqrt{3} - \sec^{-1}(-2) \) is equal to \( \frac{\pi}{3} \).
The function \( y = \sin x \) is increasing in \( \left[ 0, \frac{\pi}{2} \right] \).
The value of \( \cos^{-1} \left( \cos \frac{2\pi}{3} \right) \) is equal to:
Principal value of \( \sin^{-1}(1) \) is:
Range of the function \( \cos^{-1} \):
Write \( \cot^{-1}\left\{\frac{1}{\sqrt{x^2-1}}\right\}; x>1 \) in the simplest form.
Find the principal value of \( \sec^{-1}(-\sqrt{2}) \).
The value of \( \tan^{-1}\sqrt{3} - \sec^{-1}(-2) \) is :
Range of function \( \cos^{-1} x \) is:
Principal value of \( \sin^{-1}(1) \) is: