solwe that costeta/1-sinteta+1-sinteta/costeta=2secteta
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Step-by-step explanation:
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
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