Use a sum or difference formula to find the exact value of t

Use a sum or difference formula to find the exact value of the following.

sin pi/5 cos 2pi/15+ cos pi/5 sin 2pi/15

Solution

sin(pi/5) + cos (2pi/15) + cos(pi/5)sin(2pi/15)

This is of the form

sinA cos B + cos A sin B which is equal to sin (A+B)

so we get

sin(pi/5 + 2pi/15)=sin(5pi/15)=sin(pi/3) =sqrt 3/2