Prove that `(sinx-cosx+1)/(sinx+cos-1)=secx+tanx`. – InterviewSolution

InterviewSolution

1.	Prove that `(sinx-cosx+1)/(sinx+cos-1)=secx+tanx`.
Answer» `(sinx-cosx+1)/(sinx+cosx-1)=((sin^2x)-(cosx-1)^2)/((sinx+cosx-1)^2)` `=(2cosx-2cos^2x)/(2+2sinxcosx-2cosx-2sinx)` `=(2cosx(1-cosx))/(2(1-sinx)(1-cosx))` `=(cosx)/(1-sinx)=((1+sinx))/cosx=secx+tanx`

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