# Math Help - trig manipulating

1. ## trig manipulating

Does anyone have any idea how the solution changed $sin5\theta+sin\theta$ into $2sin(3\theta)cos(2\theta)$ been trying for ages and just can't see it? thanks

2. ok this come from

sin(a+b) = sina cosb + sinb cosa
sin(a-b) = sina cosb - sinb cosa

find the sum of two

sin(a+b) + sin(a-b) = 2 sina cosb

let a+b = x and a-b =y ..........
solve this ( find the value of a , b with respect of x .y )

a = (x+y)/2
b = (x-y)/2

now we have
sinx + siny =2 sin((x+y)/2) cos ((x-y)/2)

finish