Question

Докажите тождество
$cos2a+sin2a=(sin a+cos a)^{2} -2 sin^{2} a$

Answer 1

Ответ:

$(sin\alpha + cos\alpha )^{2} - 2sin^{2}\alpha = sin^{2}\alpha + 2sin\alpha cos\alpha + cos^{2}\alpha - 2sin^{2}\alpha = cos^{2}\alpha - sin^{2}\alpha + 2sin\alpha cos\alpha = cos2\alpha + sin2\alpha$