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Math Help - verifying trigonometric identities

  1. #1
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    verifying trigonometric identities

    I've been trying to figure this out for hrs now, somebody please assist me.
    sin^3 alpha + cos^3 aplha/ sin alpha + cos alpha = 1- sin alpha cos alpha
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  2. #2
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    Quote Originally Posted by dmak263 View Post
    I've been trying to figure this out for hrs now, somebody please assist me.
    sin^3 alpha + cos^3 aplha/ sin alpha + cos alpha = 1- sin alpha cos alpha
    \frac{(sin^3(\alpha) + cos^3(\alpha))}{(sin(\alpha)+cos(\alpha))}

    Remember that

    a^3 +b^3 = (a+b)(a^2+b^2-ab)

    Put a =sin(alpha) , b = cos(alpha)

    Remembering that

    sin^2(alpha)+cos^2(alpha) = 1
    -----------------------------------------
    So the fraction becomes

    <br />
\frac{(sin(\alpha) + cos(\alpha))(1-sin(\alpha)cos(\alpha))}{(sin(\alpha)+cos(\alpha))  }

    Now this =
    (1-sin(\alpha)cos(\alpha))

    Adarsh
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  3. #3
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    thank you.
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