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amber15

  • 3 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

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  1. calculusfunctions
    • 3 years ago
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    \[\frac{ 1 }{ 1+\sin \theta }+\frac{ 1 }{ 1-\sin \theta }\] 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
    • 3 years ago
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    thank you

  3. amber15
    • 3 years ago
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    so the answer is D

  4. calculusfunctions
    • 3 years ago
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    You mean B, don't you?

  5. amber15
    • 3 years ago
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    OOPS yes

  6. calculusfunctions
    • 3 years ago
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    Good! Don't I get a medal? lol

  7. amber15
    • 3 years ago
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    yes you get a medal and thank you

  8. calculusfunctions
    • 3 years ago
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    Haha! I was just trying to be funny but thank you!

  9. amber15
    • 3 years ago
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    you did good on explaining tho

  10. calculusfunctions
    • 3 years ago
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    Thank you!

  11. rosedewittbukater
    • 2 years ago
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    @amber15 do you remember if this answer was correct?

  12. amber15
    • 2 years ago
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    yes it is correct

  13. rosedewittbukater
    • 2 years ago
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    Thank you so much!

  14. amber15
    • 2 years ago
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    your welcome

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