Why is this equation equal to another equation?

[mapa]

x = (2vsin(theta)cos(theta))/g = (vsin2(theta))/g

v = null velocity

x = distance

g = gravity

How is the first equation equal to the second one?
How the sin2(theta) come to be and where did the cos(theta) go?

 

[Nabeshin]

Trigonometric identity:

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

 

[mapa]

thank you

 

[GRDixon]

Trigonometric identity:

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

Or more generally, sin(A+B)=sin(A)cos(B)+cos(A)sin(B).
Also handy to know: cos(A+B)=cos(A)cos(B)-sin(A)sin(B).