Question

Упростить выражения ( смотреть скриншот ниже )

Answer 1

a)

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

б)

$\frac{cos2\alpha(1-cos2\alpha)}{sin3\alpha-sin\alpha} *\frac{sin4\alpha}{cos3\alpha-cos5\alpha }= \frac{cos2\alpha (1-cos2\alpha)}{2*cos2\alpha*sin\alpha }*\frac{sin4\alpha }{-2*sin4\alpha*(-sin\alpha)}=$$=\frac{1-cos2\alpha }{2sin\alpha}*\frac{1 }{2sin\alpha}=\frac{cos^2\alpha+sin^2\alpha-(cos^2\alpha-sin^2\alpha)}{4sin^2\alpha}=\frac{cos^2\alpha+sin^2\alpha-cos^2\alpha+sin^2\alpha}{4sin^2\alpha}=$$=\frac{2sin^2\alpha }{4sin^2\alpha }=\frac{1}{2}$