CJC Sigma Notations Tutorial Q4

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Timothy Gan

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CJC Sigma Notations Tutorial Q4

Let $\text{f}(r)=\frac{\sin \left[ (2r+1)\theta  \right]}{\cos \theta }$, where $r$ is positive integer.


Show that $\text{f}(r)-\text{f}(r-1)=A\cos \left( Br\theta \right)\tan \left( \theta \right)$, where $A$ and $B$ are to be determined.


By using the result in part (a), show that

$\cos 2\theta +\cos 4\theta +…+\cos 2N\theta =\frac{1}{2}\left[ \frac{\sin \left[ \left( 2N+1 \right)\theta \right]}{\sin \theta }-1 \right]$.

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Published: 27th July 2022

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