Question

Prove that:

$tan\theta =cot\theta -2cot2\theta$

Answer 1

$\tan \theta =\cot \theta -2\cot 2\theta$

R.H.S $=\cot \theta -2\cot 2\theta$

$=\frac{1}{\tan \theta }-\frac{2}{\tan 2\theta }$

$=\frac{1}{\tan \theta }-\frac{2(1-{\tan }^2\theta )}{2\tan \theta }$

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

$=\tan \theta$

$=$ L.H.S.