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:
$\frac{1-sin \alpha }{1-sin^2 \alpha } + \frac{1+sin \alpha }{1-sin^2 \alpha} = \frac{2}{1-sin^2 \alpha}$

Finally, we can use the trig identities: $1-sin^2 \alpha =cos^2 \alpha$ and $sec \alpha = \frac{1}{cos \alpha }$ to simplify our trig expression:
$\frac{2}{cos^2\alpha}=2sec^2 \alpha$

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