Simplify a LHS of the trigonometric equation to obtain RHS Is this equality correct? If so, how to simplify the following expression on the LHS to get RHS:
$$\frac{\sin(x+\frac{nh}{2})  \sin(\frac{(n+1)h}{2})}{\sin\frac{h}{2}} +\sin(x+(n+1)h)=\frac{\sin(x+\frac{ (n+1)h}{2})  \sin(\frac{(n+2)h}{2})}{\sin \frac{h}{2}}$$
Anybody?

The formula is equivalent to 
$$
\sin(x+\frac{nh}2) \sin((n+1)\frac h2) +
\sin(x+(n+1)h)\sin \frac h2 = \sin(x + (n+1)\frac h2) \sin((n+2)\frac h2)
$$
Now use the formula
$$
\cos(A-B) - \cos(A+B) = 2\sin A\sin B
$$
This is equivalent to
$$
\cos(x-\frac h2) - \cos(x + nh + \frac h2) +
\cos(x+nh+\frac h2) - \cos(x+nh+3\frac h2)
\\= 
\cos(x - \frac h2) - \cos(x + (n+1)h + \frac h2)
$$which is true.
