Question

Упростите a) sina/2sin^2a/2 б) cos2a+sin^2a

Answer 1

$\sf a)~ \dfrac{\sin \alpha}{2sin^2\frac{\alpha}{2}}=\dfrac{2\sin\frac{\alpha}{2}\cos\frac{\alpha}{2}}{2\sin^2\frac{\alpha}{2}}=\dfrac{\cos\frac{\alpha}{2}}{\sin\frac{\alpha}{2}}={\rm ctg}\, \frac{\alpha}{2}\\ \\ \\ b)~ \cos2\alpha+\sin^2\alpha=\cos^2\alpha-\sin^2\alpha+\sin^2\alpha=\cos^2\alpha$