Question

Simplify the expression by using a double-angle formula. 2 sin 31°cos 31°

Answer 1

The double angle formula for the sine is

$\sin(2x) = 2\sin(x)\cos(x)$

The right hand side is exactly your expression, where $x = 31^\circ$

So, rewriting the expression from right to left, we have

$2\sin(31^\circ)\cos(31^\circ) = \sin(2\cdot 31^\circ) = \sin(61^\circ)$