Question

How do you use the sum to product formulas to write the sum or difference `sin5theta-sin3theta` as a product?

Answer 1

2cos4thetasintheta#

Explanation:

Use the trig identity:

`sin a - sin b = 2cos ((a + b)/2)sin ((a - b)/2)`

In this case, we have `a=5theta` and `b=3theta`:

Hence, `(a+b)/2=(5theta+3theta)/2=(8theta)/2=4theta` and

`(a-b)/2=(5theta-3theta)/2=(2theta)/2=theta`

Hence, `sin5theta-sin3theta=2cos4thetasintheta`