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Math Help - Verifying Triogonomic Identies (Double Angle)

  1. #1
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    Verifying Triogonomic Identies (Double Angle)

    Hi All,

    I am stuck on these two problems. Basically, I understand the double angle identities, but not when sin or cos is square (i.e. sin^2(2x), etc)

    Here are the problems...

    1. -1/2(sec^2(x) = -2sin^2(x)csc^2(2x)

    2. 1/2(sin(4x)) = 2sinxcosx - 4sin(sin^3(x))cos(x)

    If my notation is screwy let me know...

    Any help is appreciated. Thanks!
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  2. #2
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    Quote Originally Posted by lziz View Post
    Hi All,

    I am stuck on these two problems. Basically, I understand the double angle identities, but not when sin or cos is square (i.e. sin^2(2x), etc)

    Here are the problems...

    1. -1/2(sec^2(x) = -2sin^2(x)csc^2(2x)

    2. 1/2(sin(4x)) = 2sinxcosx - 4sin(sin^3(x))cos(x)

    If my notation is screwy let me know...

    Any help is appreciated. Thanks!
    Is Q1. -\frac{1}{2\sec^2{x}} or -\frac{1}{2}\sec^2{x}?


    Is Q2. \frac{1}{2\sin{(4x)}} or \frac{1}{2}\sin{(4x)}?
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    The latter for both questions. Also, aren't they the same thing anyway...?
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  4. #4
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    Quote Originally Posted by lziz View Post
    The latter for both questions. Also, aren't they the same thing anyway...?
    No they aren't.

    The latter are the equivalent of

    -\frac{\sec^2{x}}{2}

    and

    \frac{\sin{(4x)}}{2}.
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