Question

5. Prove that
$\frac{sin2 \alpha }{1 + cos2 \alpha } = tan \alpha$
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Answer 1

Answer:

$\frac{ \sin(2 \alpha ) }{1 + \cos(2 \alpha ) } = \tan( \alpha ) \\ lhs \: = \frac{ \sin(2 \alpha ) }{1 + \cos(2 \alpha ) } \\ = \frac{2 \sin( \alpha ) \cos( \alpha ) }{2 { \cos( \alpha ) }^{2} } \\ = \frac{ \sin( \alpha ) }{ \cos( \alpha ) } \\ = \tan( \alpha ) \\ = rhs \: \\ proved$