Thread: Trick to solve ??

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 aren't obvious ones such as , and only one of them is top-heavy ( ), which can be simplified to , which again is not a very obvious one. There's no algebraic tricks as far as I can see.