Question 870187
(cos x)/ ( 1 + sin x) + ( cos x )/(1 - sin x) =  2 sec x



(cos x)/ ( 1 + sin x) + ( cos x )/(1 - sin x) 

(cosx(1-sinx)+cos x(1+sin x))/(1-sin^2x)

(cosx-cosx.sinx)+cos x+cosx.sin x))/(1-sin^2x)

2cosx/cos^2x

2/cos x
2sec x

proved