2sin^2x+cos^2x=1 (Cosx+sinx)^2=cos2x

Question

2sin^2x+cos^2x=1

(Cosx+sinx)^2=cos2x

Answer 1

(Cosx+sinx)^2=cos2x

cos^2x +2sinxcosx+sin^2x=cos2x

sin2x+1-cos2x=0

2sinxcosx+sin^2x+cos^2x-cos^2x+sin^2x=0

2sinx(sinx+cosx)=0

sinx=0

x=ПN

sinx=-cosx/ /cosx

tgx=-1

x=-п/4+пN