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Math Help - Intergration

  1. #1
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    Intergration

    How is the step (red-boxed) formed?
    Intergration-q4.jpg
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  2. #2
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    Using the trig identity \sin^2 \theta + \cos^2 \theta = 1

    Then: \sqrt{1-\sin^2 \theta} = \sqrt{\cos^2 \theta} = \cos \theta


    Since there is a \cos \theta on both the denominator and numerator, they cancel out.
    Then by using power reducing formulas:

    \sin^2 \theta = \dfrac{1-\cos(2\theta)}{2}
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  3. #3
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    \sin^2 \theta = \frac{1-cos 2\theta}{2} is the standard power reducing formula which is worth memorizing for a calculus class since it is used so often.

    You can derive it by writing \cos 2\theta in terms of \sin^2 \theta and solving for \sin^2 \theta.
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