Question

решить уравнение:

 

cos^2 x + cos^2 2x+ cos^2 3x = 3/2

Answer 1

                                                       Решение:

 

2cos^2 x + 2cos^2 2x+ 2cos^2 3x = cos^2(x)+sin^2(x)+cos^2(2x)+sin^2(2x)+cos^2(3x)+sin^2(3x)
cos2x+cos4x+cos6x=2cos4xcos2x+cos4x=cos4x(2cos2x+1)=0.
cos4x=0 x=П/8+Пl/4
cos2x=-1/2
2x=2/3П+2Пk  x=П/3+Пk
2x=4/3П+2Пk  x=2П/3+Пk.