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Math Help - sin(x)/tan(x) = cos(x)?

  1. #1
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    sin(x)/tan(x) = cos(x)?

    Been working a little problem here for a while, the whole thing looks like this:

    Simplify:

    sin(x)/tan(x) + cos(x)tan(x)

    I know the right side can be simplified to sin(x), but im not sure about the left. I put it into terms of cosine and sine, making it: sin(x)/sin(x)/cos(x)

    My thought process here was to then multiply by the reciprocal, which would end with the sin(x)'s cancelling out and leaving just cos(x).

    Can anyone verify this?
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  2. #2
    ynj
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    Quote Originally Posted by Lewong View Post
    Been working a little problem here for a while, the whole thing looks like this:

    Simplify:

    sin(x)/tan(x) + cos(x)tan(x)

    I know the right side can be simplified to sin(x), but im not sure about the left. I put it into terms of cosine and sine, making it: sin(x)/sin(x)/cos(x)

    My thought process here was to then multiply by the reciprocal, which would end with the sin(x)'s cancelling out and leaving just cos(x).

    Can anyone verify this?
    yes,sinx/tanx=cosx
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  3. #3
    Senior Member pacman's Avatar
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    Simplify: sin(x)/tan(x) + cos(x)tan(x), then

    sin(x)/tan(x) + cos(x)tan(x) = (sin x)/(sin x / cos x) + cos x ( sin x / cos x)

    = (sin x)(cos x / sin x) + cos x ( sin x / cos x)

    = cos x + sin x
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  4. #4
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    Thanks so much guys! I was pretty sure I had this right, but I just couldn't find anywhere that verified it.
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