Question

1+sin 2a/cos 2a=tg (п/4+a)

Answer 1

$\frac{1+sin2 \alpha }{cos2 \alpha } = \frac{cos ^{2}+sin ^{2} \alpha +2sin \alpha cos \alpha }{cos ^{2} \alpha -sin ^{2} \alpha } = \frac{(cos \alpha +sin \alpha ) ^{2} }{(cos \alpha -sin \alpha )(cos \alpha +sin \alpha )} = \frac{cos \alpha +sin \alpha }{cos \alpha -sin \alpha } =$

$= \frac{ \sqrt{2}sin( \frac{ \pi }{4}+ \alpha ) }{ \sqrt{2}cos( \frac{ \pi }{4}+ \alpha ) } =\frac{sin( \frac{ \pi }{4}+ \alpha ) }{ cos( \frac{ \pi }{4}+ \alpha ) } =tg( \frac{ \pi }{4} + \alpha )$