What is the simplification of $\frac{\sin^2 x}{(1+ \sin^2 x +\sin^4 x +\sin^6 x + \cdots)} \space \text{?}$
What is the simplification of $\frac{\sin^2 x}{(1+ \sin^2 x +\sin^4 x +\sin^6 x + \cdots)}$?
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sequences-and-series
trigonometry
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0You can enclose LaTeX in `$`-signs. – 2011-02-09
2 Answers
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Assuming that $x \notin \frac{\pi}{2} + \pi \mathbb{Z}$ you can write $q = \sin^{2}{x}$ with $|q| < 1$ and use the geometric series $\sum_{n=0}^{\infty} q^{n} = \frac{1}{1-q}$.
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0@Mr D: Note that you still have to consider the two cases $\sin{x} = \pm 1$ – 2011-02-09
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What does $1 + \sin^2 x + \sin^4 x + \sin^6 x + ....$ simplify to?
Or better, what does $1 + x^2 + x^4 + x^6 + ....$ simplify to?
Or better, what does $1 + x + x^2 + x^3 + ....$ simplify to?