Question

Математики! Помогите.
Докажите тождество:

Answer 1

$\displaystyle sin(\frac{\pi }{2} -6\alpha )=cos6\alpha$

$\displaystyle cos(\pi +4\alpha )=-cos4\alpha$

$\displaystyle sin(\pi -6\alpha )=sin6\alpha$

$\displaystyle cos(\frac{3\pi }{2} +4\alpha )= sin4\alpha$

$\displaystyle cos(2\pi +10\alpha )=cos10\alpha$

$\displaystyle \frac{(cos6\alpha +cos4\alpha )(sin6\alpha -sin4\alpha )}{1+cos10\alpha } =$

$=\displaystyle \frac{( 2cos5\alpha *cos\alpha ) *(2sin\alpha *cos5\alpha ) }{1+cos^{2} 5\alpha -sin^{2} 5\alpha } =\frac{( 2cos5\alpha *cos5\alpha ) *(2sin\alpha *cos\alpha ) }{cos^{2} 5\alpha+cos^{2} 5\alpha } =$

$\displaystyle =\frac{( 2cos5\alpha *cos5\alpha ) *(2sin\alpha *cos\alpha ) }{2cos^{2} 5\alpha } =2sin\alpha *cos\alpha = sin2\alpha$

sin2α=sin2α