помогите решить. (cosx - sinx)^2 - cos2x = 1

Question

помогите решить.

(cosx - sinx)^2 - cos2x = 1

Answer 1

(cosx - sinx)^2=cos^2x-2cosx*sinx+sin^2x

cos^2x-2cosx*sinx+sin^2x-cos2x=1

cos2x=cos^2x-sin^2x

cos^2x-2cosx*sinx+sin^2x-(cos^2x-sin^2x)=1

cos^2x-2cosx*sinx+sin^2x-cos^2x+sin^2x=1

-2cosx*sinx+2sin^2x=1

2sin^2x-2cosx*sinx=1

sinx(2sinx-2cosx)=1

sinx=1

x=π/2+2πk

sinx*cosx=1/2
2sinxcosx= 1
sin2x=1
2x=π/2+2πk 
x=π/4+πk

 

Answer 2

1-sin2x-cos2x=1

-sin2x-cos2x=0

tg2x=-1

x=-п/8+пk/2