List of top Mathematics Questions on Inverse Trigonometric Functions asked in CUET (UG)

Simplify the inverse trigonometric expression to find its principal value: \[ \tan^{-1}\left(\frac{1}{2}\right) + \tan^{-1}\left(\frac{1}{3}\right) \] 

Find the domain of the function \( f(x)=\sin^{-1(3x-1) \).}
Evaluate the principal value of the inverse trigonometric expression: \( \sin^{-1}\left(\sin\frac{2\pi}{3}\right) \)
Find the value of the composite inverse trigonometric expression: \( \cot^{-1}\left[2\cos\left(2\sin^{-1}\frac{1}{2}\right)\right] \)
If \(\tan^{-1}\left(\frac{2}{3 - x + 1}\right) = \cot^{-1}\left(\frac{3}{3x + 1}\right)\), then which one of the following is true?