How does one solve an inequality such as the following:
$\sin^{2}(x+y) > \sin^{2}(x) + \sin^{2}(y)$
I can do this:
$(\sin(x)\cos(y) + \sin(y)\cos(x))^{2} > \sin^{2}(x) + \sin^{2}(y)$
$\sin(x)^{2}\cos(y)^{2} + \sin(y)^{2}\cos(x)^{2} + 2\sin(x)\sin(y)\cos(x)\cos(y) > \sin^{2}(x) + \sin^{2}(y)$
$2\sin(x)^{2}\sin(y)^{2} < 2\sin(x)\sin(y)\cos(x)\cos(y)$
The next logical step would be to divide out $\sin(x)\sin(y)$, but I think that causes problems if $\sin(x)\sin(y) < 0$