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Thread: Proving Identities

  1. #1
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    Proving Identities

    how can you prove this ..


    1. sin² [theta] + cos² [theta]/cos² [theta] = |1/cos [theta]|²
    2. 1-cos²[theta]/sin [theta] = sin [theta]_
    3. 1+cot²[theta]/csc ²[theta]=1
    4. csc² [theta]-1/csc²[theta]=cos²[theta]
    5. cot [theta] – 1 =csc [theta] – sec [theta]/ sec [theta]
    6. cos [theta] / sec [theta] + tan [theta] = 1-sin [theta]
    7. csc²[theta] = _cos ² [theta] + cot² [theta] + sin² [theta]
    8. 2 cos² [theta]-1 =cos (4th power) [theta] –sin (4th power) [theta]
    9. cos [theta]/1+sin [theta] + cos [theta] /1-sin [theta] = 2/ cos theta
    10. sin (4th power) [theta]-1/cos ² [theta]=cos² [theta] -2

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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by geleen09 View Post
    how can you prove this ..


    1. sin² [theta] + cos² [theta]/cos² [theta] = |1/cos [theta]|²
    2. 1-cos²[theta]/sin [theta] = sin [theta]_
    3. 1+cot²[theta]/csc ²[theta]=1
    4. csc² [theta]-1/csc²[theta]=cos²[theta]
    5. cot [theta] – 1 =csc [theta] – sec [theta]/ sec [theta]
    6. cos [theta] / sec [theta] + tan [theta] = 1-sin [theta]
    7. csc²[theta] = _cos ² [theta] + cot² [theta] + sin² [theta]
    8. 2 cos² [theta]-1 =cos (4th power) [theta] –sin (4th power) [theta]
    9. cos [theta]/1+sin [theta] + cos [theta] /1-sin [theta] = 2/ cos theta
    10. sin (4th power) [theta]-1/cos ² [theta]=cos² [theta] -2

    Put brackets in so we are not guessing what you mean.

    What have you done, for instance with #1

    You should know Pythagoras's theorem (\sin(\theta))^2+(\cos(\theta))^2=1

    CB
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  3. #3
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    For #2 as well, you just need to realise that \cos^2{\theta} = 1-\sin^2{\theta}.
    For #3: 1+\cot^2{\theta} = \csc^2{\theta}. The same idea goes for #3.
    Similar ideas for the rest of them. Take care of the brackets, though, or learn the latex.
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  4. #4
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    can you help to solve those??
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