How do you prove that costheta/(1-sintheta) + costheta/(1+sintheta) = 2 /costheta?

1 Answer
Mar 8, 2018

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Explanation:

LHS : cos theta/(1-sin theta)+costheta/(1+sintheta)

=(costheta(1+sintheta)+costheta(1-sintheta))/((1-sintheta)(1+sin theta))->common denominator

=(costheta+sinthetacostheta+costheta-sinthetacostheta)/(1-sin^2theta)

=(costheta+cancel(sinthetacostheta)+costheta-cancel(sinthetacostheta))/(1-sin^2theta)

=(2costheta)/cos^2theta->use the property sin^2theta+cos^2theta=1

=(2cancelcostheta)/cos^cancel2theta

=2/costheta

=RHS