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