Write cos 2 x cos 3x as a sum of two trigonometric functions

cos 2x cos 3x

cos A + cos B=2 cos((A+B)/2) cos((A-B)/2)

It can also be written as

1/2(cos A + cos B)=cos((A+B)/2) cos((A-B)/2)

comparing the given expression with the formula we get

A+B/2=3x and A-B/2=2x

A+B=6x and A-B=4x

A=5x and B=x

Therefore the required expression is

1/2(cos 5x + cosx)