Question

Помогите решить уравнение cos^4x + cos^4(x-pi/4)=1/4

Answer 1

(1+сos2x)²/4+(1+cos(2x-π/2))²/4=1/4*((1+cos2x)²+(1+sin2x)²)=1/4
(1+cos2x)²+(1+sin2x)²=1
1+2cos2x+cos²2x+1+2sin2x+sin²2x=1
3+2cos2x+2sin2x=1
2(cos2x+sin2x)=-2
cos2x+sin2x=-1
cos²x-sin²x+2sinxcosx+sin²x+cos²x=0
2cos²x+2sinxcosx=0/cos²x≠0
1+tgx=0
tgx=-1
x=-π/4+πn