Verify the identity

cosx/1+sinx + 1+sin/cosx = 2sec x

Ill assume its the first one.

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

= cos^2 x + (1 + sin x) ^2 / cos x (1 + sin x)

= cos^2 x + sin^2x + 1 + 2sinx / cos x (1 + sin x)

= 1 + 1 + 2sinx / cos x (1 + sin x) (because sin^2x + cos^2 x = 1)

= 2 (1 + sin x) / cos x (1 + sin x) = 2 / cos x = 2 sec x