Prove the following:
(i) $\tan ^{-1} 1+\cos ^{-1}\left(-\frac{1}{\sqrt{2}}\right)=\pi$
(ii) $\sin ^{-1} \frac{1}{\sqrt{2}}-3 \sin ^{-1} \frac{\sqrt{3}}{2}=-\frac{3 \pi}{4}$
(iii) $\sin ^{-1}\left(-\frac{1}{2}\right)+\cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right)=\frac{2 \pi}{3}$
(iv) $\operatorname{cosec}^{-1}(-1)+\cot ^{-1}\left(-\frac{1}{\sqrt{3}}\right)=\frac{\pi}{6}$
(v) $\cos ^{-1}\left(-\frac{1}{2}\right)+\sin ^{-1}\left(-\frac{1}{2}\right)=\frac{\pi}{2}$
(vi) $\cot ^{-1}(\sqrt{3})-\sin ^{-1}\left(-\frac{1}{2}\right)=\frac{\pi}{3}$
(vii) $\tan ^{-1} 1-\cot ^{-1}(-1)=\frac{\pi}{2}$
(viii) $\tan ^{-1} 1+\cot ^{-1} 1+\sin ^{-1} 1=\pi$.