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anonymous

  • one year ago

Use basic identities to simplify the expression. (cos of theta^2 / sin of theta ^2) + csc θ sin θ

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  1. Nnesha
    • one year ago
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    \[\huge\rm \frac{ \cos^2 \theta }{ \sin ^2 \theta } +\csc \theta \sin \theta \] like this ?

  2. Nnesha
    • one year ago
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    write csc in terms of sin or cos what's the definition of csc ?? like sec = 1/cos csc = ??

  3. anonymous
    • one year ago
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    csc = 1/sin theta would I multiply sin theta * 1/sin theta and get 1?

  4. Nnesha
    • one year ago
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    yes that's right :-)

  5. Nnesha
    • one year ago
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    and cos /sin = what ? :-) remember tan and cot are reciprocal of each other

  6. anonymous
    • one year ago
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    (1/ sec theta)^2 /(1 / csc theta)^2?? I'm not really sure how to simplify that :(

  7. Nnesha
    • one year ago
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    well that's right but simple way is to change cos/sin to cot \[\tan =\frac{ \sin }{ \cos } ~~\cot=\frac{ \cos }{ \sin }\]

  8. Nnesha
    • one year ago
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    so cos^2 theta over sin ^2 theta = cot^2 theta

  9. anonymous
    • one year ago
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    is there a way to simplify that further?

  10. Nnesha
    • one year ago
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    yes

  11. Nnesha
    • one year ago
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    \[\huge\rm\color{blue}{ \frac{ \cos^2 \theta }{ \sin ^2 \theta } }+\color{reD}{\csc \theta \sin \theta} \] \[\large\rm \color{blue}{ \cot^2 \theta} +\color{red}{1} = ???\] which is equal to what ??it's an identity

  12. anonymous
    • one year ago
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    pythagoras? csc^2 theta?

  13. Nnesha
    • one year ago
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    yes right cot^2 + 1 = csc^2 x

  14. anonymous
    • one year ago
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    omg thank you! identities confuse me so much :)

  15. Nnesha
    • one year ago
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    my pleasure :-) and practice!! :-)

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