(cos3x+cosx)^2+(sin3x+sinx)^2  упростите

(cos 3x+cos x)^2 + (sin 3x+sin x)^2= (2cos[latex] \frac{3x+x}{2} [/latex] cos [latex] \frac{3x-x}{2} [/latex])^2 + (2sin[latex] \frac{3x+x}{2} [/latex] cos[latex] \frac{3x-x}{2} [/latex])^2= (2cos 2x cos x)^2 + (2sin 2x cos x)^2= 4 cos^2 2x cos^2 x+ 4 sin^2 2x cos^2 x= 4cos^2 x(cos^2 2x+sin^2 2x)=4 cos^2 x