How do you prove (cosx/(1 + sinx)) + (cosx/(1 - sinx)) = 2secx?

1 Answer
Mar 6, 2018

See Below

Explanation:

LHS: cosx /(1+sinx) + cos x/(1-sinx)

=(cosx(1-sinx)+cosx(1+sinx))/(1-sin^2x)-->common denominator

=(cosx-sin x cos x+cosx+sinx cos x)/cos^2x

=(cosxcancel(-sin x cos x)+cosx+cancel(sinx cos x))/cos^2x

=(2cosx)/cos^2x

=(2cancelcosx)/cos^cancel2x

=2/cosx

=2*1/cosx

=sec x

=RHS