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Math Help - Proving Trig Identities

  1. #1
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    Post Proving Trig Identities

    Help proving these identities


    1.) tanX-tanY / 1+tanX = cotY-cotX / cotXcotY+1

    2.) sin5X + Sin3X / sin5X-sin3X = tan4X / tanX
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  2. #2
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    Hello orochimaru700
    Quote Originally Posted by orochimaru700 View Post
    Help proving these identities


    1.) tanX-tanY / 1+tanX = cotY-cotX / cotXcotY+1

    2.) sin5X + Sin3X / sin5X-sin3X = tan4X / tanX
    Can I suggest first that:

    • you should copy the question down carefully; and:
    • either learn how to write these things using LaTeX (lots of information available on this web-site); or:
    • use brackets correctly.
    I'm sure you mean for number (1):
    (tanX-tanY) / (1+tanXtanY) = (cotY-cotX) / (cotXcotY+1)
    Anyway, enough of my ranting. Divide top-and-bottom of the fraction on the LHS by \tan X\tan Y:
    \frac{\tan X - \tan Y}{1+ \tan X\tan Y}
    =\frac{\dfrac{\tan X}{\tan X\tan Y} - \dfrac{\tan Y}{\tan X\tan Y}}{\dfrac{1}{\tan X\tan Y}+ \dfrac{\tan X\tan Y}{\tan X\tan Y}}

    =\frac{\dfrac{1}{\tan Y} - \dfrac{1}{\tan X}}{\dfrac{1}{\tan X}\dfrac{1}{\tan Y}+ \dfrac{1}{\tan X\tan Y}}

    =\frac{\cot Y - \cot X}{\cot X \cot Y +1}

    For (2) use the sum-to-product formulae. For example, the numerator becomes 2\sin 4x\cos x. Use a similar formula on the denominator, simplify and you're there.

    Can you complete this now?

    Grandad
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  3. #3
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    thnks for the advice and solution grandad, i'll try solve for # 2
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