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anonymous

  • one year ago

Simplify the trigonometric expression

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  1. DecentNabeel
    • one year ago
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    @EllenJaz17 what is the expression

  2. anonymous
    • one year ago
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    \[\frac{ \sin ^{2} }{ 1-}\]

  3. anonymous
    • one year ago
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    its supposed to be sin^2theta/1-cos theta

  4. DecentNabeel
    • one year ago
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    the answer is 1

  5. DecentNabeel
    • one year ago
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    correct @EllenJaz17

  6. anonymous
    • one year ago
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    \[\frac{ \sin ^{2}\theta }{1-cos }\]

  7. anonymous
    • one year ago
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    and theta is after the cos.

  8. anonymous
    • one year ago
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  9. anonymous
    • one year ago
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  10. anonymous
    • one year ago
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  11. DecentNabeel
    • one year ago
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    \[\mathrm{Use\:the\:following\:identity}:\quad \:1=\cos ^2\left(x\right)+\sin ^2\left(x\right)\] \[=\frac{\sin ^2\left(θ\right)}{\cos ^2\left(θ\right)-\cos ^2\left(θ\right)+\sin ^2\left(θ\right)}\] \[\frac{\sin ^2\left(θ\right)}{-\cos ^2\left(θ\right)+\cos ^2\left(θ\right)+\sin ^2\left(θ\right)}\] \[\mathrm{Add\:similar\:elements:}\:-\cos ^2\left(θ\right)+\cos ^2\left(θ\right)=0\] \[=\frac{\sin ^2\left(θ\right)}{\sin ^2\left(θ\right)+0}\] \[=\frac{\sin ^2\left(θ\right)}{\sin ^2\left(θ\right)}\] =1

  12. DecentNabeel
    • one year ago
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    this is the 1 problem

  13. anonymous
    • one year ago
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  14. anonymous
    • one year ago
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    Those are my answer options

  15. DecentNabeel
    • one year ago
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    ohhhhhh you needed just answer @EllenJaz17

  16. anonymous
    • one year ago
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    yeah. Those are my options A-D in the attachments

  17. anonymous
    • one year ago
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    Would the answer be C?

  18. anonymous
    • one year ago
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    @DecentNabeel

  19. misty1212
    • one year ago
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    HI!!

  20. anonymous
    • one year ago
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    hey

  21. misty1212
    • one year ago
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    is it just \[\huge \frac{1-\sin(x)}{\cos(x)}\]

  22. anonymous
    • one year ago
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    So it's b?

  23. misty1212
    • one year ago
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    no i am still trying to figure out what the original question one

  24. misty1212
    • one year ago
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    was

  25. anonymous
    • one year ago
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    Simplify it

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  26. misty1212
    • one year ago
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    can you repost the original one

  27. DecentNabeel
    • one year ago
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    \[\mathrm{Simplify}\:\frac{1-\sin \left(θ\right)}{\cos \left(θ\right)}:\quad \left(1-\sin \left(θ\right)\right)\sec \left(θ\right)\]

  28. misty1212
    • one year ago
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    \[\huge \frac{\sin^2(\theta)}{1-\cos(\theta)}\]

  29. misty1212
    • one year ago
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    we can do a couple things if that is the original question

  30. anonymous
    • one year ago
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    Simplify the trigonometric expression (is the question)

  31. misty1212
    • one year ago
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    perhaps the easiest it to rewrite \(\sin^2(\theta)\) as \(1-\cos^2(\theta)\) then factor

  32. anonymous
    • one year ago
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    Use the identity sin^2 = 1-cos^2. Then factor it into (1+cos)(1-cos). Then cancel

  33. misty1212
    • one year ago
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    \[\frac{\sin^2(\theta)}{1-\cos(\theta)}=\frac{1-\cos^2(\theta)}{1-\cos(\theta)}=\frac{(1+\cos(\theta))(1-\cos(\theta))}{1-\cos(\theta)}=1+\cos(\theta)\]

  34. anonymous
    • one year ago
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    Is that the final answer?

  35. misty1212
    • one year ago
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    not sure if that is an answer choice, but if it is, pick that one

  36. anonymous
    • one year ago
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    It is! Thank you!

  37. misty1212
    • one year ago
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    \[\color\magenta\heartsuit\]

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