# Rewrite as an expression that doesn't contain a fraction: (3tanX)/(1-cosX)

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Expert Answers

beckden | Certified Educator

`(3tanx)/(1-cosx)*(1+cosx)/(1+cosx)=(3tanx(1+cosx))/(1-cos^2x)=(3tanx+3tanxcosx)/(sin^2x) `

`tanx = sinx/cosx`

So

`(3tanx)/(1-cosx) = 3(sinx/cosx+sinx/cosx*cosx)/sin^2x=3(1/sinx1/cosx+1/sinx)`

`cscx=1/sinx` and `secx=1/cosx` so

`(3tanx)/(1-cosx)=3cscx(secx+1)`