Express the following as product of sines or cosines function cos5x+cos3x

Question

accept this my question 

Answer 1

cos5x+cos3x

cosx+cosy=2cos([x+y]/2)cos([x-y])/2

cos5x+cos3x=2cos([5x+3x]/2)cos([5x-3x])/2)

cos5x+cos3x=2cos4xcosx

Answer 2

cos5x + cos3x = (1/2)(cos(5x + 3x) + cos(5x - 3x)) = (1/2)(cos8x + cos 2x)