Question

can you guys please show me the steps toward verifying this identity:
cos(-x)/1+sin(-x) = sec x + tan x

Answer 1

Is it \(\large \frac{\cos(-x)}{1+\sin(-x)}?\)

Answer 2

yes

Answer 3

First you have to know that \(\cos(-x)=\cos(x)\text{ and } \sin(-x)=-\sin(x)\).
\[{\cos(-x) \over 1+\sin(-x)}={\cos(x) \over 1-\sin(x)}={(1+\sin(x))\cos(x) \over 1-\sin^2(x)}={(1+\sin(x))\cos(x) \over \cos^2(x)}\]
\[={1+\sin(x) \over \cos(x)}={1 \over \cos(x)}+{\sin(x) \over \cos(x)}=sex(x)+\tan(x).\]

Answer 4

\(\large \sec(x)+\tan(x)\)*

Answer 5

ohh okay!
thank you so much! c:

Answer 6

"c:" << nice! :D

Answer 7

ahah c:
thanks!

Answer 8

You're welcome!