Question

factor:
4tan^2x-(4)/(cotx)+sinx(cscx)

Answer 1

Well factor out the 4, and sinx(cscx) = 1, see where that gets you. You will probably see some straightforward identities after that.

Answer 2

And to be clear, is this (4tan^2(x)/cot(x)) + sin(x)(csc(x)) or is the sin(x)(csc(x)) in the denominator?

Answer 3

You have 4(tan^2 x -1)/(cot x+1) as sinx =1/cosec x
=4(1+tanx)(1-tan x)(1+1/tanx ) as cot x=1/tan x
=4(tanx)(1-tan x) (Taking LCM and cancelling 1 +tan x