Question

Simplify the trigonometric expression.

Answer 1

1/(1+sin theta) + 1/(1-sin theta)

THe answer is letter D. 2 sec^2 theta

Hope it help! Goodluck!

Answer 2

First we are going to find the common denominator of both fractions. To do that, we are going to multiply their denominators:

`(1+sin \alpha )(1-sin \alpha )=1-sin^2 \alpha`

Now we can rewrite our expression using the common denominator:

`(1-sin \alpha )/(1-sin^2 \alpha ) + (1+sin \alpha )/(1-sin^2 \alpha) = (2)/(1-sin^2 \alpha)`

Finally, we can use the trig identities:
`1-sin^2 \alpha =cos^2 \alpha` and
`sec \alpha = (1)/(cos \alpha )` to simplify our trig expression:

`(2)/(cos^2\alpha)=2sec^2 \alpha`

We can conclude that the correct answer is the fourth one.