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)`