$\cos \left[\cos ^{-1}\left(-\frac{1}{7}\right)+\sin ^{-1}\left(-\frac{1}{7}\right)\right]$ is equal to

If $0 < x < 1$,then $\sqrt{1+x^2} [\{x \cos (\cot ^{-1} x)+\sin (\cot ^{-1} x)\}^2-1]^{\frac{1}{2}}$ is equal to

$\tan^{-1}(-2) - \tan^{-1}(3)$ is equal to

If $\sin^{-1} \frac{3}{5} + \cos^{-1} \frac{12}{13} = \sin^{-1} C$,then $C =$

If $\cos^{-1}\left(\frac{x}{a}\right) + \cos^{-1}\left(\frac{y}{b}\right) = \alpha$,then $\frac{x^2}{a^2} - \frac{2xy}{ab}\cos \alpha + \frac{y^2}{b^2} = $

The value of $\cot ^{-1}(-\sqrt{3})-\tan ^{-1} \sqrt{3}$ is equal to . . . . . . .