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Math Help - trigonometry Addition Formulae (iv)

  1. #1
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    trigonometry Addition Formulae (iv)

    I have worked out how to do it, just I need to know how to solve it without calculator.

    Find the exact value of:
    2 cos²15 - 1

    this is what i did:

    2 cos²15 - 1 so
    = cos²15 + sin²15 = 1 side note: sin²15 = 1 - cos²15 hence: 2 cos²15 - 1

    then i did:
    2 cos²15 - 1 would initially be: cos²15 + sin²15
    = cos(15 + 15)
    = cos 15 x cos 15 - sin 15 x sin 15
    = root 3 / 2


    What i wanna know is, i could not of done this without a calculator...
    What is the alternative method?
    (sorry if i made this very confusing)
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  2. #2
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    \begin{array}{rcl}<br />
 2\cos ^2 (A) - 1 & = & \cos (2A) \\ <br />
 2\cos ^2 (15^o ) - 1 & = & \cos (30^o ) \\ <br />
  & = & \frac{{\sqrt 3 }}{2} \\ <br />
 \end{array}
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  3. #3
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    can you give me step by step for:
    1 - 2 sinē 22.5
    answer = 1/root 2

    i know it will involve something like 22.5x2 = 45......
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  4. #4
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    1 - 2\sin ^2 (A) = \cos (2A)
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