Question

Prove that : $\tan 8\theta -\tan 6\theta -\tan 2\theta =\tan 8\theta .\tan 6\theta .\tan 2\theta .$

Answer 1

It is known that $6\theta +2\theta =8\theta$

Apply tan both sides,

$\tan \left(6\theta +2\theta \right)=\tan 8\theta$

$\frac{\tan 6\theta +\tan 2\theta }{1-\tan 6\theta \tan 2\theta }=\tan 8\theta$

$\tan 6\theta +\tan 2\theta =\tan 8\theta -\tan 8\theta \tan 6\theta \tan 2\theta$

$\tan 8\theta -\tan 6\theta -\tan 2\theta =\tan 8\theta \tan 6\theta \tan 2\theta$