Question

Упростить выражение: sin²((пи/4)+α) - sin²(пи/4) - α)

Answer 1

$Sin^{2}(\frac{\pi }{4}+\alpha)-Sin^{2}(\frac{\pi }{4}-\alpha)=Sin^{2}[\frac{\pi }{2}-(\frac{\pi }{4}-\alpha)] -Sin^{2}(\frac{\pi }{4}-\alpha)=\\\\=Cos^{2}(\frac{\pi }{4}-\alpha)-Sin^{2}(\frac{\pi }{4}-\alpha)=Cos(\frac{\pi }{2}-2\alpha)=\boxed{Sin2\alpha}$