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Thread: Trigonometric Expressions

  1. May 3rd 2012, 12:02 AM #1
    DjNito
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    Trigonometric Expressions

    Hey guys I need some help with these two different equations. It is to simplify the expressions:

    Equation 1:

    9sinx/cos^2x * cosxsinx-3cosx/sin^2x-9

    and the second equation is:

    sin^4xcosx/cos^4xsinx

    Thanks in advance!!
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  2. May 3rd 2012, 05:34 AM #2
    Soroban
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    Re: Trigonometric Expressions

    Hello, DjNito!

    These require basic Algebra (factoring and reducing).
    Exactly where is your difficulty?

    These are not equations . . . they are expressions.
    Be precise.

    \frac{9\sin x}{\cos^2\!x}\cdot \frac{\cos x\sin x - 3\cos x}{\sin^2\!x - 9}

    Factor: . \frac{9\sin x}{\cos^2\!x}\cdot \frac{\cos x(\sin x - 3)}{(\sin x - 3)(\sin x + 3)}

    Reduce: . \frac{9\sin x}{\cos x(\sin x + 3)}



    \frac{\sin^4\!x\cos x}{\cos^4\!x\sin x}

    Reduce: . \frac{\sin^4x\cos x}{\sin x\cos^4\!x} \;=\;\frac{\sin^3\!x}{\cos^3\!x}

    Simplify: . \left(\frac{\sin x}{\cos x}\right)^3 \;=\;\tan^3\!x
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