prove that (1-sinx)/cosx+cosx/(1-sinx)=2sec x

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