cosx/ 1+sinx = secx − tanx
cosx
________ = secx - tan x
1 + sin x
= 1/cosx - sin x/ cosx
= ( 1 - sin x) / cos x
= cos x (1 -sin x) / cos^2x
= cosx ( 1 - sinx) / ( 1 -sin^2 x)
= cosx (1 - sin x) / [ (1-sin x) ( 1 + sinx ) ]
= cosx / ( 1 + sin x)