Question

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

Answer 1

\[\frac{ 1 }{ 1+\sin \theta }+\frac{ 1 }{ 1-\sin \theta }\]

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!

Answer 2

thank you

Answer 3

so the answer is D

Answer 4

You mean B, don't you?

Answer 5

OOPS yes

Answer 6

Good! Don't I get a medal? lol

Answer 7

yes you get a medal and thank you

Answer 8

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

Answer 9

you did good on explaining tho

Answer 10

Thank you!

Answer 11

@amber15 do you remember if this answer was correct?

Answer 12

yes it is correct

Answer 13

Thank you so much!

Answer 14

your welcome