Question

(1+sin a+cos a)(sin a+cos a-1)

Answer 1

$sin2\alpha$

Объяснение:

$(1+sin\alpha+cos\alpha)(sin\alpha+cos\alpha-1)=(sin\alpha+cos\alpha+1)(sin\alpha+cos\alpha-1)=$

$=(sin\alpha+cos\alpha)^{2}-1^{2}=sin^{2}\alpha+2 \cdot sin\alpha \cdot cos\alpha+cos^{2}\alpha-1=2 \cdot sin\alpha \cdot cos\alpha+$

$+sin^{2}\alpha+cos^{2}\alpha-1=sin2\alpha+1-1=sin2\alpha;$