COS(X)+COS(2X)+COS(6X)+COS(7X)=4COS(X/2)*COS(5X/2)*COS(4X)

Question

COS(X)+COS(2X)+COS(6X)+COS(7X)=4COS(X/2)*COS(5X/2)*COS(4X)

Answer 1

(cosx+cos7x)+(cos2x+cos6x)=2cos4xcos3x+2cos4xcos2x=2cos4x(cos3x+cos2x)=2cos4x(2cos5x/2 cosx/2)=4COS(X/2)*COS(5X/2)*COS(4X)