Question

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

Answer 1

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