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Math Help - TRIG Identities and Equations

  1. #1
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    TRIG Identities and Equations

    These are the problems I have trouble with while doing a practice on this topic.

    1. Factor the expression and use fundamental identities to simplify:
    cos^(2)x csc^(2)x - cos^(2)x

    2. Find all solutions in the interval [0 , 2pi)
    tan^(2)θ = (-3/2)secθ

    3. Find an expression that completes the identity
    [2sin^(2)x + cos(2x)] / csc(x) =

    It would be helpful if u could explain step by step. I'm not just looking for answers. Thanks
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  2. #2
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    Re: TRIG Identities and Equations

    In the first one, take out \cos^2x as a factor, what do you get?

    For the second, create a quadratic using \tan^2\theta = \sec^2\theta -1 what do you get?
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  3. #3
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    Re: TRIG Identities and Equations

    Here is #2.
    TRIG Identities and Equations-trig.jpg
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  4. #4
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    Re: TRIG Identities and Equations

    In 3 use the identity cos2x=1-2sin^(2)x
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  5. #5
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    Re: TRIG Identities and Equations

    Hello, Crysland!

    \text{3. Find an expression that completes the identity,}

    . . \frac{2\sin^2\!x + \cos2x}{\csc x}\:=\:\_\_\_

    Replace \cos2x with \cos^2\!x - \sin^2\!x

    \frac{2\sin^2\!x + \cos2x}{\csc x} \;=\;\frac{2\sin^2\!x + (\cos^2\!x - \sin^2\!x)}{\csc x}

    . . . . . . . . . . . =\; \frac{\overbrace{\sin^2\!x + \cos^2\!x}^{\text{This is 1}}}{\csc x}

    . . . . . . . . . . . =\; \frac{1}{\csc x}


    . . . . . . . . . . . =\;\sin x
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  6. #6
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    Re: TRIG Identities and Equations

    thanks so much. I'm still stuck with #1.
    I got 2 answers, cos^2x*cot^2x and cos^4x/sin^2x
    but don't know which one is correct and simplified.
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  7. #7
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    Re: TRIG Identities and Equations

    Both your answers equal one another (because cotx=cosx/sinx)
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  8. #8
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    Re: TRIG Identities and Equations

    So Are They Correct?
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  9. #9
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    Re: TRIG Identities and Equations

    Yes they are correct.
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