Re: HSC 2013 2U Marathon
\sin^2 1^{\circ}+ \sin^2 89^{\circ} =1 + .... +\sin^2 44^{\circ}+ \sin^2 46^{\circ}= 44 $your left with$ \ \ sin^2 45^{\circ}+ \sin^2 90^{\circ}= 1+\frac{1}{2}} therefore \ \ 44 + 1+\frac{1}{2}= 45 + \frac{1}{2}}
Edit: sin^2 45^{\circ} \ \ is\ \ \frac{1}{2}\ \ $so...