Question

Найдите sin x * cos x ,если sin x + cos x = 1

Answer 1

$sinx+cosx=1\\\\(sinx+cosx)^2=1\\\\sin^2x+2sinx\cdot cosx+cos^2x=1\\\\1+2sinx\cdot cosx=1\\\\2sinx\cdot cosx=0\\\\sinx\cdot cosx=0$