The double angle formula for the sine is
[tex] \sin(2x) = 2\sin(x)\cos(x) [/tex]
The right hand side is exactly your expression, where [tex] x = 31^\circ [/tex]
So, rewriting the expression from right to left, we have
[tex] 2\sin(31^\circ)\cos(31^\circ) = \sin(2\cdot 31^\circ) = \sin(61^\circ) [/tex]
