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  1. Similar Triangles
  2. areas
  3. pythagoreanTheorem
  4. circles
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  6. threeDimensionalGeometry
  7. trigonometry
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  9. miscellaneous
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Exercise 380
If $\sum_{n=0}^\infty\cos^{2n}\theta=8$, what is the value of $\cos2\theta$?
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Solution
  1. The geometric series sums to $\frac1{1-\cos^2\theta}=\frac1{\sin^2\theta}=8$, so $\sin^2\theta=\frac18$.
  2. $\cos2\theta=1-2\sin^2\theta=1-\frac14=\boxed{\dfrac34}$.
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