# CJC Sigma Notations Tutorial Q4

## Timothy Gan

This is Tim. Tim loves to teach math. Tim seeks to improve his teaching incessantly! Help Tim by telling him how he can do better.
##### CJC Sigma Notations Tutorial Q4

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

(a)

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.

(b)

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

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

## Students Only

Our H2 Math Tuition includes

• Question Bank with Video solutions to 1400+ questions
• Online Portal
• H2 Math Summary Notes
• Structured Curriculum and Notes
Free Stuff
Pure Math
Statistics

## Students Only

Our H2 Math Tuition includes

• Question Bank with Video solutions to 1400+ questions
• Online Portal
• H2 Math Summary Notes
• Structured Curriculum and Notes
Free Stuff
Pure Math
Statistics