trigonometry

Question

use a sum to product identity to evaluate the expression:      sin 3 alpha + sin 8 alpha.  thanks

Answer 1

sin(3α) + sin(8α) => using sum as product identity below:

 

sin A + sin B = 2 sin [(A + B)/2] cos [(A − B)/2]

 

sin(3α) + sin(8α)

 

= 2 sin [(3α +8α)/2] cos [(3α −8α)/2]

 

= 2 sin [(11α)/2] cos [(−5α)/2]

 

= 2 sin [(11α)/2] cos [(5α)/2] => answer