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Math Help - proving identities

  1. #1
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    Smile proving identities

    how would i prove that csc x / cot x + tan X = cos???
    it has been disturbing me for almost 3 days,, ..

    hope you guys can help me...

    thanks..
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  2. #2
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    Quote Originally Posted by riasantos View Post
    how would i prove that csc x / cot x + tan X = cos???
    it has been disturbing me for almost 3 days,, ..

    hope you guys can help me...

    thanks..
    We shouldn't have to waste time figuring out if you mean csc x / (cot x + tan X) = cos or (csc x / cot x) + tan X = cos. Use brackets to remove the ambiguity!
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  3. #3
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    Smile provind trigonometric identities..

    umm.. okay.. thanks for the reply..

    then the equation must be...

    [csc (x) / cot (X) ] + tan (x) = cos (x)

    how would i prove it???
    thanks.. ^^
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  4. #4
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    Quote Originally Posted by riasantos View Post
    umm.. okay.. thanks for the reply..

    then the equation must be...

    [csc (x) / cot (X) ] + tan (x) = cos (x)

    how would i prove it???
    thanks.. ^^
    Are you sure you wrote the identity correctly?
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  5. #5
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    Smile

    umm.. yes. why?? is it wrong???
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  6. #6
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    Quote Originally Posted by riasantos View Post
    umm.. yes. why?? is it wrong???
    Yeah, that's not an identity. Counterexample: \frac{\pi}{4}

    sin\left(\frac{\pi}{4}\right) = cos\left(\frac{\pi}{4}\right) = \frac{1}{\sqrt2}

    tan\left(\frac{\pi}{4}\right) = cot\left(\frac{\pi}{4}\right) = 1


    Spoiler:
    \left[\frac{1}{sin\left(\frac{\pi}{4}\right)} \div cot\left(\frac{\pi}{4}\right)\right] + tan\left(\frac{\pi}{4}\right) = \sqrt{2} \div 1 + 1 = \sqrt{2}+1 \neq \frac{1}{\sqrt2}<br />
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  7. #7
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    Smile

    thanks.. ^^
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  8. #8
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    Quote Originally Posted by riasantos View Post
    thanks.. ^^
    However:

    \frac{csc(x)}{cot(x)+tan(x)} = cos(x) is an identity
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