Prove that \(\frac{\tan 69^o+\tan 66^o}{1-\tan 69^o\tan 66^o}=-1\)

Prove that \(\cos18^o-\sin18^o=\sqrt{2}.\sin27^o\)

If \(\tan^2x=2\tan^2\phi+1\), prove that \(\cos2x+sin^2\phi=0\)

Evaluate : \(\cos\left[\frac{\pi}{3}-\cos^{-1}\left(\frac{1}{2}\right)\right]\)

Find the principal value of \(\cos^{-1}\left(\frac{-1}{\sqrt2}\right)\)