Question

решить уравнение (sin-cos)^2=2

Answer 1

sin^2x-2sinx*cos x+cos ^2 x=2

1-2sin x*cos x=2

-2sin x*cos x=1

sinx*cos x=-0.5

sin 2x=-1

2x=-П/2+2П*к

х=-П/4+П*к

Answer 2

$sin^2x-2sinxcosx+cos^2x=2$

$-2sinxcosx+1=2$

$sin2x=-1$

$2x=-frac{pi}{2}+2pi n$

$x=-frac{pi}{4}+pi n$