Question

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

Answer 1

4(1+cos2x)²/4-2cos2x-1/2*(2cos²2x-1)=
=1+2cos2x+cos²2x-2cos2x-cos²2x+1/2=1 1/2=3/2

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