## amber15 2 years ago Simplify the trigonometric expression. 1/1+ sin theta + 1/1-sin theta A, 2 cos^2 theta B. 2 sec^2 theta C. 2 csc^2 theta D. 2 cot^2 theta A,2 cos^2 theta B. 2 sec ^2 theta C. 2 csc^2 theta D, 2 cot^2 theta my answer is B can some one tell me if im correct i know C and A are not correct answers

1. calculusfunctions

$\frac{ 1 }{ 1+\sin \theta }+\frac{ 1 }{ 1-\sin \theta }$ The LCD (least common multiple of the denominators) is (1 + sin θ)(1 − sin θ). Hence $\frac{ 1 }{ 1+\sin \theta }+\frac{ 1 }{ 1-\sin \theta }$ $=\frac{ 1-\sin \theta }{(1+\sin \theta)(1-\sin \theta) }+\frac{ 1+\sin \theta }{ (1+\sin \theta)(1-\sin \theta) }$ $=\frac{ 1-\sin \theta +1+\sin \theta }{ (1+\sin \theta)(1-\sin \theta) }$ $=\frac{ 2 }{ 1-\sin ^{2}\theta }$ $=\frac{ 2 }{ \cos ^{2}\theta }$ $=2\sec ^{2}\theta$ I hope that helps!

2. amber15

thank you

3. amber15

4. calculusfunctions

You mean B, don't you?

5. amber15

OOPS yes

6. calculusfunctions

Good! Don't I get a medal? lol

7. amber15

yes you get a medal and thank you

8. calculusfunctions

Haha! I was just trying to be funny but thank you!

9. amber15

you did good on explaining tho

10. calculusfunctions

Thank you!

11. rosedewittbukater

@amber15 do you remember if this answer was correct?

12. amber15

yes it is correct

13. rosedewittbukater

Thank you so much!

14. amber15