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

1 Answer
Aug 18, 2016

L.H.S=R.H.S

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

=2sectheta

L.H.S=R.H.S