Solve $\sin(5A) + \cos(5A)\sin(A) - \cos(3A) = 0$ How do you solve this equation for A:
$~~\sin(5A) + \cos(5A)\sin(A) - \cos(3A) = 0$
I've tried expanding it many times, but I can't seem to be able to reduce it to a format I can work with. Is there a simpler method of solution than repeated expansion?

Try using $\cos{A} = \sin\frac{\pi}{2}-A$ and the $\sin{A} + \sin{B}$ or $\cos{A} + \cos{B}$ formulas. You can also write $2 \cos{A}\sin{B} = \sin(A+B) - \sin(A-B)$, which actually will reduce $\cos{5A}\cdot\sin(A)$.
