Inverse Trigonometric Functions - Trigonometry - Mathematics Previous Year Questions

Find the value of \(\cos ^{-1}\left(\frac{4}{5}\right)+\tan ^{-1}\left(\frac{3}{5}\right)\).

Using the principal values, the value of \(\sin ^{-1}\left\{\sin \frac{5 \pi}{6}\right\}+\tan ^{-1}\left\{\tan \frac{\pi}{6}\right\}\) is equal to

If \(\tan ^{-1} y=\tan ^{-1} x+\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)\), where \(|x|< \frac{1}{\sqrt{3}}\) then value of \(y\) is

If \(\cos ^{-1} x-\cos ^{-1} \frac{y}{2}=\alpha\) where \(-1 \leq x \leq 1, -2 \leq y \leq 2, x \leq \frac{y}{2}\), then for all \(x, y, 4 x^2-4 x y \cos \alpha+y^2\) is equal to

If \(\left(\sin ^{-1} x\right)^2-\left(\cos ^{-1} x\right)^2=a \pi^2\), then the range of \(a\) is

The equation \(3 \cos ^{-1} x-\pi x-\pi / 2=0\) has

If \(\cot ^{-1}(y)=\cot ^{-1}(x)+\cot ^{-1}\left(\frac{x^2-1}{2 x}\right)\), then the value of \(y\) is

\(\tan ^{-1}\left(\frac{1}{5}\right)+\tan ^{-1}\left(\frac{1}{7}\right)+\tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{8}\right)\) equals to

The value of \(\sin ^{-1}\left\{\cot \left(\sin ^{-1} \sqrt{\frac{2-\sqrt{3}}{4}}+\cos ^{-1} \frac{\sqrt{12}}{4}+\sec ^{-1} \sqrt{2}\right)\right\}\) is

The sum of the infinite terms of the series $\cot ^{-1}\left(1^2+\frac{3}{4}\right)+\cot ^{-1}\left(2^2+\frac{3}{4}\right)$ $+\cot ^{-1}\left(3^2+\frac{3}{4}\right)+\ldots$ is equal to