Question

30 Points!

Verify the identity (Picture Below):


Can you help me not only answer this but go through all the steps as well that would be great, thanks.

Answer 1

`(cos \: x)/(1 + sin \: x) + (1 + sin \: x)/(cos \: x) = \frac{ {cos}^(2)x + {(1 + sin \: x)}^(2) }{cos \: x \: (1 + sin \: x)} \\ = \frac{ {cos}^(2)x + 1 + 2sin \: x \: + {sin}^(2)x }{cos \: x \: (1 + sin \: x)} = (2 + 2sin \: x)/(cos \: x \: (1 + sin \: x)) \\ = (2(1 + sin \: x))/(cos \: x \: (1 + sin \: x)) \: = (2)/(cos \: x) = 2sec \: x`