List of top Mathematics Questions on Inverse Trigonometric Functions asked in Bihar Board XII

Find \( \tan^{-1} (\sqrt{3}) - \cot^{-1} (-\sqrt{3}) \).
Find \( \sin \left( \sin^{-1} \frac{2}{3} \right) + \tan^{-1} \left( \tan \frac{3\pi}{4} \right) \).
Find \( \tan^{-1} \left( \frac{1}{2} \right) + \tan^{-1} \left( \frac{1}{3} \right) \).
If \( \sin \left( \sin^{-1} \frac{1}{5} \right) + \cos^{-1} x = 1 \), find \( x \).
What is \( \cos^{-1} x + \sec^{-1} 1 \)?
Find \( \cot^{-1} \left( \tan \frac{\pi}{7} \right) \).
Find \( \cos^{-1} \left( \cos \frac{8\pi}{5} \right) \).
Find \( \tan^{-1} (-\sqrt{3}) \).
\(\int \frac{4 \tan^{-1} x}{1 + x^2} \, dx \)
\(\frac{d}{dx} \left[ 2 \tan^{-1} x \right] \)
\(\frac{d}{dx} \left( \sin^{-1} 2x \right)\)
For \(|x|\le1\), \(2\tan^{-1}x=\ \ ?\)
For \(x\in\mathbb R\), \(\cot^{-1}x=\ \ ?\)
\(\tan^{-1}\!\left(\dfrac{x+y}{1-xy}\right)=\ \ ?\)
\(\sin^{-1}\!\big(\sin \tfrac{2\pi}{3}\big)=\ \ ?\)

\(\sin\!\big(\sin^{-1}\tfrac12\big)=\) ?

\(\sin^{-1}x+\sin^{-1}y=\) (principal values)

For \(x\in[-1,1]\), evaluate \(\ \sin\!\big(2(\sin^{-1}x+\cos^{-1}x)\big)\).

For \(x\in\mathbb{R}\), compute \(\csc\!\big(\tan^{-1}x+\cot^{-1}x\big)\).

If \(|x|\ge1\), then \(\tan\!\left[\dfrac{2}{3}\big(\tan^{-1}x+\cot^{-1}x\big)\right]=\) ?