cosx/(1+sinx) + cosx/(1-sinx) = 2secx
R.S.
[cosx(1-sinx)+cosx(1+sinx)]/[(1+sinx)(1-sinx)] ? :S
good first step.
now continue, expand the top, the bottom is difference of squares
so
LS
= (cosx - sinxcosx + cosx + sinxcosx)/(1-sin^2 x)
= 2cosx/cos^2 x
= 2/cosx
= 2secx
= RS.