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Thread: Write trig expression as an algebraic expression containing u and v

  1. #1
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    Write trig expression as an algebraic expression containing u and v

    I'm stuck on this one:
    Cos(tan^-1u+tan^-1v)
    I know you can use cos(a+b)=cosacosb-sinasinb but not sure what to do after.
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  2. #2
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    Re: Write trig expression as an algebraic expression containing u and v

    Hey av66.

    I think you may want to draw two triangles with angles u and v in them and use the same ideas that you use to solve something like cos(tan^(-1)[u]) or sin(tan^(-1)[u]).
    Thanks from av66 and topsquark
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  3. #3
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    Re: Write trig expression as an algebraic expression containing u and v

    Thanks! I think I got it now. Is the answer?:
    (1-uv)/(√1+u^2√1+v^2)
    Last edited by av66; Nov 4th 2014 at 10:51 PM.
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  4. #4
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    Re: Write trig expression as an algebraic expression containing u and v

    I haven't done the working out but if you want to get the opinions of other readers (including myself) then show us the working out so we can follow and evaluate it.
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  5. #5
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    Re: Write trig expression as an algebraic expression containing u and v

    I understand, here's a picture of my work. If you could please check the next question also.

    Write trig expression as an algebraic expression containing u and v-20141105_133155.jpg
    Last edited by av66; Nov 5th 2014 at 10:46 AM.
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  6. #6
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    Re: Write trig expression as an algebraic expression containing u and v

    Hello, av66!

    Is the answer? .$\displaystyle \frac{1-uv}{\sqrt{1+u^2}\sqrt{1+v^2}}$
    Yes . . . Good work!
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