доказать тождество 4 cos^4x - 2 cos 2x - 1/2 cos 4x = 3/2
решить уравнение sin^4x cos^2x - cos^4x sin^2x = cos 2x

4(1+cos2x)²/4-2cos2x-1/2*(2cos²2x-1)==1+2cos2x+cos²2x-2cos2x-cos²2x+1/2=1 1/2=3/2sin²xcos²x(sin²x-cos²x)=cos2x-1/4*sin²2x*cos2x=cos2xcos2x+1/4*sin²2xcos2x=0cos2x(1+1/4sin²2x)=0cos2x=0⇒2x=π/2+πn⇒x=π/4+πn/21+1/4*sin²2x=0sin²x=-4 нет решения