We have to verify: sqrt [(1 + sin x)/(1 - sin x)] = (1 + sin x)/|cos x|

sqrt [(1 + sin x)/(1 - sin x)]

=> sqrt [(1 + sin x)(1 + sin x)/(1 - sin x)(1 + sin x)]

=> sqrt [(1 + sin x)^2/(1 - (sin x)^2)]

...

## 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.

We have to verify: sqrt [(1 + sin x)/(1 - sin x)] = (1 + sin x)/|cos x|

sqrt [(1 + sin x)/(1 - sin x)]

=> sqrt [(1 + sin x)(1 + sin x)/(1 - sin x)(1 + sin x)]

=> sqrt [(1 + sin x)^2/(1 - (sin x)^2)]

=> sqrt [(1 + sin x)^2/(cos x)^2]

=> (1 + sin x)/|cos x|

**This verifies that sqrt [(1 + sin x)/(1 - sin x)] = (1 + sin x)/|cos x|**