Prove:!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Question

 

tanx+secx=cosx/1-sinx

Answer 1

using trignometric quotient identies

tanx=sinx/cosx;secx=1/cosx

tanx+secx=(sinx/cosx)+(1/cosx)

                  =(1+sinx)/cosx

Multiply denominator and numerator with 1-sinx

=(1+sinx)(1-sinx)/(cosx)(1-sinx)

=(1-sin^2x)/(cosx)(1-sinx)

Recall the trignometric Pythagoras 1-sin^2x=cos^2x

=cos^2x/(cosx)(1-sinx)

=cosx/1-sinx

Simplified expression is cosx/1-sinx

I hope that helps u