Question

Prove that $\frac{\cos 27+\sin 27}{\cos 27-\sin 27}=\tan 72$

Answer 1

L.H.S$=\frac{\cos {27}^o+\sin 27}{\cos {27}^o-\sin 27}$

$=\frac{1+\frac{\sin 27}{\cos 27}}{1-\frac{\sin 27}{\cos 27}}$

$=\frac{1+\tan {27}^o}{1-\tan {27}^o}$

$=\frac{\tan {45}^o+\tan {27}^o}{1-\tan {45}^o\times \tan {27}^o}$

$=\left(\tan {45}^o+{27}^o\right)$

$=\tan {72}^o=R.H.S\left(proved\right).$