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DanielleElmas [232]
3 years ago
10

Simplify the trigonometric expression.

Mathematics
2 answers:
ryzh [129]3 years ago
6 0
1/(1+sin theta) + 1/(1-sin theta) 

THe answer is letter D. 2 sec^2 theta

Hope it help! Goodluck! 
Natasha_Volkova [10]3 years ago
5 0
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.
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