I'm doing some algorithms research and I need to prove that a large equation (obtained from taking a partial derivative) is always positive. I'm not a mathematician so I haven't been able to make heads or tails of it.
Is there any way to show that the following equation is greater than zero \begin{align*} &-b \sin(t -a t + 2 r ) \\ &+ \sin(a t - t + 2 b (\pi - r - t) ) \\ &+ b \sin(t + a t + 2 r ) \\ &- \sin(t+at + 2b(\pi - r - t) ) \\ &+ (b+1) \sin(t - a t) \\ &+ (1-b)\sin(t+at) \end{align*}
if we know the following information for the variables \begin{alignat*}{2} 0&<a& &<1 \\ 0&<b& &<1 \\ 0^{\circ}&<t& &<45^{\circ} \\ 0^{\circ}&<r& &<45^{\circ} \end{alignat*}
I broke the equation into individual components to make it more readable, but so far I don't know if there's a strong enough connection between components (lines) of the equation to say that the result is always positive, though I suspect it will be.