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

1 Answer
Shiva Prakash M V
Jun 2, 2018

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

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