Question on proving an identity

[Lazz72]

So I'm given a problem in which I have to prove an identity. It goes:
2csc2x=csc^2xtanx

I did the problem myself and could only get to 2csc2x=2\(sin2x)= 2\(2sinxcosx). I had no idea how to get further with the problem so I looked at the answer in the back of my pre-calculus book. It said that:

2\(2sinxcosx) = 1\(sin^2x) multiplied by sinx\cosx = csc^2xtanx

I don't understand the part that says 2\(2sinxcosx)= 1\(sin^2x) multiplied by sinx/cosx. Could someone please explain to me how 2\(2sinxcosx) equals that?

 

[rl.bhat]

Hi Lazz72, welcome to PF.
2csc(2x) = 2/sin(2x) = 2/2six*cosx = 1/sinx*cos* = sinx/sinx*sinx*cosx = tanx/sin^2(x)

 

[Lazz72]

Ahh okay I understand it now, thanks!