Question

Help me evaluate : cos (π/7) + cos (2π/7) + cos (3π/7) ?

Answer 1

Evaluate the sum: `cos ((pi)/7) + cos ((2pi)/7) + cos ((3pi)/7)`

Explanation:

Apply the trig identity: `cos a + cos b = cos ((a + b)/2).cos ((a -b)/2)`

First, evaluate: `cos ((pi)/7) + cos ((3pi)/7) = cos ((2pi)/7).cos ((pi)/7)`
Next, evaluate: `cos ((2pi)/7) + cos ((2pi)/7).cos ((pi)/7)` =

`= cos ((2pi)/7)(1 + cos ((pi)/7))`