verify the identities COSX OVER 1PLUS SINX PLUS 1PLUS SINX OVER COSX IS EQUAL TO 2SEC.
cos/(1+sin) + (1+sin)/cos
cos^2/[ cos(1+sin) ] +(1+sin)^2 /[cos(1+sin)]
(cos^2 + 1 + 2 sin + sin^2)/[cos(1+sin)]
but cos^2 + sin^2 = 1
( 2 + 2 sin) /[cos(1+sin)]
2 (1+sin)/[cos(1+sin)]
2/cos
which is
2 sec