Review question

# Why is $\cos \theta + \cos (\theta + 2\pi/3) + \cos(\theta + 4\pi/3)=0$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R9782

## Question

1. Prove that $\cos(A+B)=\cos A\cos B - \sin A\sin B,$ where the angles $A$, $B$ and $A+B$ are all acute.

2. By projecting the sides of an equilateral triangle onto a certain line, prove that $\cos \theta + \cos \left(\theta + \frac{2\pi}{3}\right) + \cos\left(\theta+\frac{4\pi}{3}\right)=0$ and find the value of the expression $\sin \theta + \sin \left(\theta + \frac{2\pi}{3}\right) + \sin\left(\theta+\frac{4\pi}{3}\right).$