How do you verify the identity #costheta/(1+sintheta)+costheta/(1-sintheta)=2sectheta#?

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Answer 1 · 2016-08-18T16:32:48

#L.H.S=R.H.S#

#L.H.S=cos theta/(1+sintheta)+costheta/(1-sintheta)#

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

#=(costheta-costheta*sintheta+costheta+costheta*sintheta)/cos^2theta#

#=(costheta-cancel(costheta*sintheta)+costheta+cancel(costheta*sintheta))/cos^2theta#

#=(2costheta)/cos^2theta#

#=2/costheta#

#=2sectheta#

#L.H.S=R.H.S#