# Math Help - Trig indentity problem, I think

1. ## Trig indentity problem, I think

$3(1+\cos\frac{\pi}{9}+\cos\frac{2\pi}{9})\sin120 \pi t +3(\sin\frac{\pi}{9}+\sin\frac{2\pi}{9})\cos120 \pi t$

$= (8.638\cos\frac{\pi}{9})\sin120 \pi t+(8.638\sin\frac{\pi}{9})\cos120 \pi t$

Can anyone give me a hint about how to get from the first line to the second? I know the problem resolves to

$8.638\sin(120 \pi t + \frac{\pi}{9})$

2. ## Re: Trig indentity problem, I think

In the first bracket use a trig identity to add $1+\cos(2\pi/9),$ you should get $2\cos^{2}(\pi/9).$
Remove $\cos(\pi/9)$ as a common factor.

In the second bracket, $\sin(2\pi/9)=2\sin(\pi/9)\cos(\pi/9).$
Remove $\sin(\pi/9)$ as a common factor.

In both bracketed expressions, put in the decimal value for $\cos(\pi/9).$