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Math Help - equation using identites

  1. #1
    Senior Member furor celtica's Avatar
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    equation using identites

    solve the following equation for A, giving all the roots in the interval 0<A<360 (including 0 and 360, i don't know how to write the dash under the sign) correct to the nearest dp:
    4((sinA)^2)cosA=(tanA)^2

    ok i already know my results are wrong, i don't want the answers i just want to know where i went wrong
    so using tan=sinA/cosA, i eliminate (sinA)^2 from both sides of the equation
    which gives 4cosA=1/(cosA^2)
    => (cosA^3)=1/4
    => cosA=1/sqrt2
    A= 45, 315

    where am i wrong?
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  2. #2
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    \displaystyle 4\sin^2{A}\cos{A} = \tan^2{A}

    \displaystyle 4\sin^2{A}\cos{A} = \frac{\sin^2{A}}{\cos^2{A}}

    \displaystyle 4\sin^2{A}\cos^3{A} = \sin^2{A}

    \displaystyle 4\sin^2{A}\cos^3{A} - \sin^2{A} = 0

    \displaystyle \sin^2{A}(4\cos^3{A} - 1) = 0

    \displaystyle \sin^2{A} = 0 or \displaystyle 4\cos^3{A} - 1 = 0.

    Go from here.
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  3. #3
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    Or take roots from here...
    The same form is:

    Cos[x/2]^2*Csc[[Pi]/4 - x/2]^2 Csc[[Pi]/4 + x/2]^2*Sin[x/2]^2 (-1 + Cos[3 x]+3*Cos[x]) =0

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