Question

How do i get left side to equal right side?

(Cos x)/(1+sin x) + (cos x)/(1-sin x) = 2secx

Answer 1

LS = cosx/(1+sinx) + cosx/(1-sinx)

= ( cosx(1 - sinx) + cosx(1+sinx) )/(1 - sin^2 x)
= (cosx - sinxcosx + cosx + sinxcosx)/cos^2 x
= 2cosx/cos^2 x
= 2/cosx
= 2secx
= RS