Question

Cos8-sin8/ cos8+ sin 8 =tan 37

Answer 1

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Answer 2

Answer and Explanation:

To prove : $\frac{\cos 8-\sin 8}{\cos 8+\sin 8}=\tan 37$

Proof :

Taking LHS,

$LHS=\frac{\cos 8-\sin 8}{\cos 8+\sin 8}$

Multiply and divide by $\cos 8$

$=\frac{\frac{\cos 8}{\cos 8}-\frac{\sin 8}{\cos 8}}{\frac{\cos 8}{\cos 8}+\frac{\sin 8}{\cos 8}}$

$=\frac{1-\tan8}{1+\tan8}$

We know, $\tan 45=1$

$=\frac{\tan45-\tan8}{1+\tan45\tan8}$

This form a formula,  

$\frac{\tan a-\tan b}{1+\tan a\tan b}=\tan (a-b)$

$=\tan (45-8)$

$=\tan 37$

=RHS

Hence proved.