If $\displaystyle f(r)=\cos 2r\theta$ , simplify $\displaystyle f(r+1)-f(r)$ . Use your result to find the sum of the first n terms of the series : $\displaystyle 3\sin \theta+\sin 5\theta+\sin 7\theta+...$

For the first part , i got

$\displaystyle f(r+1)-f(r)=\cos (2r+2)\theta-\cos 2r\theta$ .. is this correct .

But from here , i couldn't relate to the second problem .