hey im trying to show that $\displaystyle sin(X+Y)sin(X-Y) = sin^2X-sin^2Y$ .
any idea how i can go with it?
basically firstly i have:
$\displaystyle
sin(X+Y)sin(X-Y)
= sinXcosY+cosXsinY \cdot sinXcosY-cosXsinY
=
$
then where can i go? cheers
hey im trying to show that $\displaystyle sin(X+Y)sin(X-Y) = sin^2X-sin^2Y$ .
any idea how i can go with it?
basically firstly i have:
$\displaystyle
sin(X+Y)sin(X-Y)
= sinXcosY+cosXsinY \cdot sinXcosY-cosXsinY
=
$
then where can i go? cheers
First, I put needed parentheses into your setup.
This can be foiled out easily, since it can be recognized as the difference of two squares. You should have
$\displaystyle \begin{aligned}\sin^2X\cos^2Y-\cos^2X\sin^2Y&=\sin^2X\left(1-\sin^2Y\right)-\left(1-\sin^2X\right)\sin^2Y\\&=\sin^2X-\sin^2X\sin^2Y-\sin^2Y+\sin^2X\sin^2Y\\&=\sin^2X-\sin^2Y\end{aligned}$
Does this make sense?