Question

(sin2a+sin2b)^2+(cos2a+cos2b)^2

Answer 1

Решение на фото......................

Answer 2

$(\sin 2\alpha+\sin 2\beta)^2+(\cos2\alpha+\cos2\beta)^2=\underbrace{\sin^22\alpha+\cos^22\alpha}_{=1}+2\sin2\alpha\sin 2\beta+\\ \\ \\ +\underbrace{\sin^22\beta+\cos^22\beta}_{=1}+2\cos2\alpha\cos2\beta=2+2(\sin2\alpha\sin2\beta+\cos2\alpha\cos2\beta)=\\ \\ \\ =2+2(\cos2\alpha\cos2\beta+\sin2\alpha\sin2\beta)=2+2\cos(2\alpha-2\beta )=4\cos^2(\alpha-\beta)$