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Math Help - Trig...Simplifying

  1. #1
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    Trig...Simplifying

    How do I simplify this problem (so that the Right Side is equal to the Left Side)?

    cosx - (cosx)/(1-tanx) = (sinx cosx)/ (sinx - cosx)
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  2. #2
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    Without telling you the entire solution, I will give you some hints. First, change everything into sines and cosines, so the tangent must equal sine/cosine. From there, you can multiply out and see the equality.
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  3. #3
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    I am going to post a scan of the work that I did...i think that I might be on the right track, but messed up somewhere...it will just take me a minute to upload...
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  4. #4
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    Please ignore 25 continued...underneath it....it is another problem
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  5. #5
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    You are right so far except your denominator has disappeared.

    It must be:
    \frac{cos x-\frac{sin x cos x}{cosx}-cos x}{1-tan x}

    The numerator can be simplified to
    \frac{cos x-sinx-cos x}{1-tan x}= \frac{-sinx}{1-tan x}

    Then as previously stated change tan x in the denominator to \frac{sinx}{cos x}
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  6. #6
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    Now I have got:
    -sinx/ 1-(sinx/cosx) What do I do now?
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  7. #7
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    -\frac{sin x}{1-\frac{sin x}{cosx}}

    -\frac{sin x}{\frac{cos x}{cos x}-\frac{sin x}{cos x}} Common denominators

    -\frac{sin x}{\frac{cos x - sin x}{cos x}}

    -sin x \cdot \frac{cos x}{cos x - sin x} Multiply the reciprocal

    -\frac{sin x \cdot cos x}{-(sin x - cos x)} Simplify the bottom

    \frac{sin x \cdot cos x}{(sin x - cos x)}=RHS
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