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

1 Answer
Nghi N.
Sep 19, 2015

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))

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