I'm currently working on a problem and stumbled on this equation that I'm unable to reduce using the standard goniometric identities. Perhaps the formula is impossible to reduce but any help is appreciated.
The formula I'm trying to reduce:
$$Av^{h}_{i}=4\sin(a)\sin(b)-\sin(a+c)\sin(b)-\sin(a)\sin(b+d)$$
[added from a comment: I've got $a=\pi ki$, $b=\pi kl$, $c=\pi k$, and $d=\pi l$, where $i$, $j$, $k$, $l$ are positive integers.]
I've tried to use the identity:
$$\sin(a+b)+\sin(a-b)=2\sin(a)\cos(b)$$
But this doesn't get me any further than a massive mess of equations. Again, perhaps the equation cannot be reduced further, but my teacher pointed out that it is indeed possible, it just takes alot of writing.
Any help is appreciated.