Question

Verify the identity
cosx/1+sinx + 1+sin/cosx = 2sec x

Answer 1

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