Пожалуйста упростите.

Решите задачу:

$sin \frac{7 \pi }{12} -sin \frac{ \pi }{12} =2sin \frac{\frac{7 \pi }{12}-\frac{\pi }{12}}{2} *cos \frac{\frac{7 \pi }{12}+\frac{\pi }{12}}{2} =2sin \frac{ \frac{6 \pi }{12} }{2}*cos \frac{ \frac{8 \pi }{12} }{2}=\\=2sin \frac{ \pi }{4}*cos \frac{ \pi }{3} =2* \frac{ \sqrt{2} }{2} * \frac{1}{2} =\frac{ \sqrt{2} }{2}$

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