
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(ab)Cos(a+b)] other then that I am lost and was wondering if someone is able to direct me the the right direction.

$\displaystyle \displaystyle\int_0^{\pi}\sin mx\sin nxdx=\frac{1}{2}\int_0^{\pi}[\cos(mn)x\cos(m+n)x]dx=$
$\displaystyle \displaystyle =\left.\frac{1}{2(mn)}\sin(mn)x\right_0^{\pi}\left.\frac{1}{2(m+n)}\sin(m+n)x\right_0^{\pi}=0$