Question

How do you simplify `tan x/ (sec x - cos x)`?

Answer 1

`tanx/(secx-cosx)=cscx`

Explanation:

`tanx/(secx-cosx)=?`
`tanx=sinx/cosx; secx=1/cosx`
`tanx/(secx-cosx)=(sinx/cosx)/(1/cosx-cosx)`
Multiplying numerator and denominator by cosx
`=sinx/(1-cos^2x)`
`1-cos^2x=sin^2x`
`tanx/(secx-cosx)=sinx/sin^2x=1/sinx=cscx`

`tanx/(secx-cosx)=cscx`