Intergration

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December 7th 2010, 12:04 AM
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Intergration

How is the step (red-boxed) formed?
Attachment 20006
December 7th 2010, 12:12 AM
Educated

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:

$\sin^2 \theta = \dfrac{1-\cos(2\theta)}{2}$
December 7th 2010, 12:15 AM
DrSteve

$\sin^2 \theta = \frac{1-cos 2\theta}{2}$ 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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