sin^4x+cos^4x-cos2x=0,5

Question

sin^4x+cos^4x-cos2x=0,5

Answer 1

(sin^2x+cos^2x)^2-2sin^2xcos^2x-cos2x=1/2
1-sin^2(2x)/2-cos2x=1/2
1-1/2(1-cos^2(2x))-cos2x=1/2
1/2cos^2(2x)-cos2x=0
cos2x(1/2cos2x-1)=0
x=П/4+Пk/2
1/2cos2x=1 нет решения |cosx|<=1<br>