What is the trick to solve these ?
1. cos (2pi/7) + cos (4pi/7) + cos (6pi/7) = ?
2. sin (pi/10) * sin (13pi/10) = ?
I believe there has to be a simple trick to solve these, but am unable to figure that so far : ( .
Any clue ?
Looks like you should plug it into a calculator from here. Most of the co-efficients of $\displaystyle \pi$ aren't obvious ones such as $\displaystyle \frac{\pi}{2}, \frac{\pi}{3}, \frac{3\pi}{2}$, and only one of them is top-heavy ($\displaystyle \frac{13}{10}$), which can be simplified to $\displaystyle \frac{3}{10}$, which again is not a very obvious one. There's no algebraic tricks as far as I can see.