Question

prove that cos 9 + sin 9 / cos 9 - sin 9 = tan 54

Answer 1

Hi Friend !!!

Here is ur answer !!!

hope it helps you ...

:-)

Answer 2

Answer and explanation:

To prove : $\frac{\cos 9+\sin 9}{\cos 9-\sin 9}=\tan 54$

Proof :

Taking LHS,

$\frac{\cos 9+\sin 9}{\cos 9-\sin 9}$

Take $\cos 9$ common from numerator and denominator,

$=\frac{\cos 9(1+\frac{\sin 9}{\cos 9})}{\cos 9(1-\frac{\sin 9}{\cos 9})}$

We know, $\tan A=\frac{\sin A}{\cos A}$

$=\frac{1+\tan 9}{1-\tan 9}$

$=\frac{\tan 45+\tan 9}{1-\tan 45\tan 9}$

Using identity, $\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\tan B}$

$=\tan (45+9)$

$=\tan 54$

= RHS

Hence proved.