cosx*cos2x*cos3x*cos4x*cos5x怎么化简?结果是多少?

=cos 2;2xcos 2;x-1 cos 2;2x cos 2;x-cos 2;2xcos 2;x =cos 2;2x cos 2;x-1 =(1 cos4x)/2 (1 cos2x)/2-1 =(1/2)(cos4x cos2x

cosx*cos2x*cos4x = 2 sinx*cosx*cos2x*cos4x / (2sinx)
= sin2x * cos2x *cos4x /(2sinx) =......= sin8x / (8sinx)
cos3x*cos5x =(1/2) ( cos8x +cos2x)
原式= (1/16) (1/sinx) [ sin8x cos8x + sin8xcos2x ]
= (1/32) (1/sinx) [ sin16x + sin10x +sin6x ]