Simplify the expression by using a Double-Angle Formula or a Half-Angle Formula. 2*sin(x/2)*cos(x/2)

Question

Simplify the expression by using a Double-Angle Formula or a Half-Angle Formula.
`2*sin(x/2)*cos(x/2)`

Answer 1

`2\sin{(x)/(2)}\cos{(x)/(2)} = sin(x)`

Explanation:

The double angle formula states that:

`sin(2a) = 2sin(a)cos(a)`

In this question:

`2\sin{(x)/(2)}\cos{(x)/(2)}`

So

`a = (x)/(2)`

Then

`2\sin{(x)/(2)}\cos{(x)/(2)} = \sin{(2x)/(2)} = sin(x)`