Express the given product as a sum containing only sines or

Express the given product as a sum containing only sines or cosines.

sin(4theta) cos(2theta)=

(simplify answer including any radicals. Use integers or fractions for any numbers in the expression.)

Solution

sin(4theta) cos(2theta) =

Use the identity : sinxcosy = (1/2)[ sin(x+y) + sin(x - y) ]

So, sin(4theta) cos(2theta) = (1/2)[sin(4theta +2theta) +sin(4theta - 2theta) ]

= (1/2)[sin6theta +sin2theta]

= sin(6theta)/2 + sin(2theta)/2