Question

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

Answer 1

Answer:

$2\sin{\frac{x}{2}}\cos{\frac{x}{2}} = \sin{x}$

Step-by-step explanation:

The double angle formula states that:

$\sin{2a} = 2\sin{a}\cos{a}$

In this question:

$2\sin{\frac{x}{2}}\cos{\frac{x}{2}}$

So

$a = \frac{x}{2}$

Then

$2\sin{\frac{x}{2}}\cos{\frac{x}{2}} = \sin{\frac{2x}{2}} = \sin{x}$