# Prove tanx=csc2x-cot2x

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`tanx = csc2x - cos2x `

`cscx = 1/sinx `

`cotx = (cosx)/(sinx)`

`==gt csc2x - cotx = 1/(sin2x) - (cos2x)/(sin2x) `

`= (1-cos(2x))/(sin2x)`

We know that:

`cos2x =1-2sin^2 x`

sin2x = 2sinxcosx

`==gt (1-(1-2sin^2x))/(2sinxcosx) `

`==gt (1-1+2sin^2 x)/(2sinxcosx) `

`==gt (2sin^2 x)/(2sinxcosx)`

Now we will reduce similar.

**==> (sinx)/(cosx)= tan(x) **..................q.e.d