Question

proved that, (sin52+cot38) /(sin38+cos 52) =tan52

Answer 1

the question is wrong

Answer 2

Answer and Explanation:

To prove : $\frac{\sin 52+\cos 38}{\sin 38+\cos 52}=\tan 52$

Proof :

Taking LHS,

$\frac{\sin 52+\cos 38}{\sin 38+\cos 52}$

$=\frac{\sin 52+\cos (90-52)}{\sin 38+\cos (90-38)}$

We know, $\cos(90-\theta)=\sin \theta$

$=\frac{\sin 52+\sin 52}{\sin 38+\sin 38}$

$=\frac{2\sin 52}{2\sin 38}$

$=\frac{\sin 52}{\sin (90-38)}$

We know, $\sin(90-\theta)=\cos \theta$

$=\frac{\sin 52}{\cos 52}$

$=\tan 52$

= RHS

Hence proved.