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Math Help - Identities

  1. #1
    Member purplec16's Avatar
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    Identities

    Prove the following identities

    sin^2xcos^2x=\frac{1}{8}(1-cos4x)

    \frac{sin u - sin v}{cos u -cos v}=-cot\frac{1}{2}(u+v)
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  2. #2
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    Quote Originally Posted by purplec16 View Post
    Prove the following identities

    sin^2xcos^2x=\frac{1}{8}(1-cos4x)

    \frac{sin u - sin v}{cos u -cos v}=-cot\frac{1}{2}(u+v)
    Use the formula
    cos(2θ) = 1 - 2sin^2(θ)
    Or 2sin^2(θ) = 1 -cos(2θ
    And sin(2θ) = 2sinθcosθ
    For second problem use
    sinA - sinB = 2cos[(A+B)/2]*sin[(A-B)/2]
    cosA - cosB = -2sin[(A+B)/2]*sin(A-B)/2]
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