# Math Help - orthogonal

1. ## orthogonal

Show that intergrate from 0 to Pi Sinmx Sinnx dx = 0 if m doesnt = n (use trig identities)

I know that the trig identity that I need to know is SinaSinb= 1/2[Cos(a-b)-Cos(a+b)] other then that I am lost and was wondering if someone is able to direct me the the right direction.

2. $\displaystyle\int_0^{\pi}\sin mx\sin nxdx=\frac{1}{2}\int_0^{\pi}[\cos(m-n)x-\cos(m+n)x]dx=$
$\displaystyle =\left.\frac{1}{2(m-n)}\sin(m-n)x\right|_0^{\pi}-\left.\frac{1}{2(m+n)}\sin(m+n)x\right|_0^{\pi}=0$