SRJC P1 Q7
Timothy Gan
SRJC P1 Q7
Let $\text{f}\left( r \right)=\frac{\sin \left[ (2r+1)\theta \right]}{\cos \theta },r\in {{\mathbb{Z}}^{+}}$.
(i)
Show that $\text{f}\left( r \right)-\text{f}\left( r-1 \right)=A\cos \left( Br\theta \right)\tan \left( \theta \right)$, where $A$ and $B$ are to be determined.
(ii)
By using the result part (i), 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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