Question

Question #737ba

Answer 1

`(sin 17x - sin 7x)/2`

Explanation:

Rewrite cos (12x).sin (5x)
Use trig identity:
`sin a - sin b = 2cos ((a + b)/2).sin ((a - b)/2)`
Find a and b, knowing:
a + b = 2(12) = 24
a - b = 2(5) = 10
Add up 2 above equations -->
2a = 34 --> a = 17
b = 24 - a = 24 - 17 = 7.
Finally,
`(sin 17x - sin 7x)/2 = cos (12x).sin (5x)`