Ask Me Help Desk - Verifying identities

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Verifying identities

sin(x+y)/(sin(x)+sin(y)=(sin(x)-sin(y))/sin(x-y)

$\frac{\sin (x+y)}{\sin x+ \sin y} = \frac{\sin x - sin y}{\sin (x-y)} :$

$\sin (x+y) \sin (x-y) = (\sin x + \sin y) (\sin x - \sin y)$

$\sin (x+y) \sin (x-y) =$
$(\sin x\cos y + \sin y\cos x)(\sin x\cos y - \sin y \cos x)=$
$\sin^2 x\cos^2y - \sin^2y\cos^2x =$
$\sin^2x(1-\sin^2y)-\sin^2y(1-\sin^2 x)=$
$\sin^2x - \sin^2x\sin^2y - \sin^2y + \sin^2x\sin^y=$
$\sin^2x-\sin^2y$

$(\sin x + \sin y) (\sin x - \sin y)=\sin^2x-\sin^2y$

Comment on lemon14's post

Thanks this was a big help !

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