Question

prove 4th question.
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Answer 1

Step-by-step explanation:

We have,

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

Divide num. and deno. by $\cos(9\degree)$

So,

$\frac{ 1+\tan(9\degree) }{1 - \tan(9\degree) }$

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

$= \tan(45\degree +9\degree)$

$= \tan(54\degree)$

$= \tan(90 \degree - 36\degree)$

$= \cot( 36\degree)$