The trigonometric identity `tan x + cos x/(1+sin x) = 1/cos x` has to be proved.

Start with the left hand side.

`tan x + cos x/(1+sin x)`

= `sin x/cos x + cos x/(1+sin x)`

= `(sin x*(1+sin x) + cos x*cos x)/(cos x*(1+sin x))`

= `(sin x +...

## Unlock

This Answer NowStart your **48-hour free trial** to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Already a member? Log in here.

The trigonometric identity `tan x + cos x/(1+sin x) = 1/cos x` has to be proved.

Start with the left hand side.

`tan x + cos x/(1+sin x)`

= `sin x/cos x + cos x/(1+sin x)`

= `(sin x*(1+sin x) + cos x*cos x)/(cos x*(1+sin x))`

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

Use the fact `sin^2x+cos^2x = 1`

= `(sin x + 1)/(cos x*(1+sin x))`

= `1/(cos x)`

**This proves **`tan x + cos x/(1+sin x) = 1/cos x`