Question

1-tgx = (sinx-cosx)^2

Answer 1

1-tgx=sin^2 x -2*sinx*cosx+cos^2 x
1-tgx=(sin^2 x+cos^2 x)-2sinx*cosx
1-tgx=1-2sinx*cosx
-tgx=-sin2x
tgx=sin2x
sinx/cosx=2sinx*cosx
1/cosx=2*cosx
1=2*cos^2x
1/2=cos^2x
cosx= +- Кор 1/2