Trig Product: Simplifying sina+sinb+sin(a+b) as a Product

[tatoo5ma]

Hello,
I have to write $${\it sina}+{\it sinb}+\sin \left( a+b \right)$$ as a product.
Here is what I began with, then I got stuck...
$$2\,\sin \left( (a+b)/2 \right) \cos \left( (a-b)/2 \right) +{\it sina}\,{\it cosb}+{\it cosa}\,{\it sinb}$$

Anyone please can help me out, that would be great, thank you!

 

[siddharth]

tatoo5ma, Instead of expanding sin(a+b), what else can you do? If you write it as a trignometric function of (a+b)/2 can you see what happens?

 

[Integral]

sure

Sin (a+b) = Sin (2(a+b)/2) = 2 cos((a+b)/2)Sin((a+b)/2)

 

[mohlam12]

yeah, then u can factor with Sin((a+b)/2) and then make cos((a-b)/2)+cos((a+b)/2) equal to 2cos(a/2)cos(b/2) and u have everythin factorized