Question

(sin2x+sinx)^2+(cos2x+cosx)^2=1

Answer 1

$(sin(2x)+sin(x))^2+(cos(2x)+cos(x))^2=1\\sin^2(2x)+2sin(2x)sin(x)+sin^2(x)+cos^2(2x)+2cos(2x)cos(x)+\\+cos^2(x)=1\\1+2sin(2x)sin(x)+sin^2(x)+2cos(2x)cos(x)+cos^2(x)=1\\2(sin(2x)sin(x)+cos(2x)cos(x))=1\\2cos(x)=-1\\cos(x)=- \frac{1}{2} \\x=+-arccos(- \frac{1}{2})+2\pi k \\x=+-(- \frac{2\pi}{3} )+2\i k$

Answer 2

Решение в прикрепленной фотографии..