Question 974679
cosx/(1+sinx)

cos x(1-sinx)/[(1+sinx)(1-sinx)]  ;; multiply by (1-sin x/1-sin x)

cosx-sinxcosx/(1-sin^2x) ;;;  1-sin^2x=cos^2x

cosx-sinxcosx/cos^2x

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

sec x - tan x.