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

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

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Answer 1 · 2015-09-19T04:48:14

Evaluate the sum: $cos (\frac{π}{7}) + cos (\frac{2 π}{7}) + cos (\frac{3 π}{7})$ $cos ((pi)/7) + cos ((2pi)/7) + cos ((3pi)/7)$

Explanation:

Apply the trig identity: $cos a + cos b = cos (\frac{a + b}{2}) . cos (\frac{a - b}{2})$ $cos a + cos b = cos ((a + b)/2).cos ((a -b)/2)$

First, evaluate: $cos (\frac{π}{7}) + cos (\frac{3 π}{7}) = cos (\frac{2 π}{7}) . cos (\frac{π}{7})$ $cos ((pi)/7) + cos ((3pi)/7) = cos ((2pi)/7).cos ((pi)/7)$
Next, evaluate: $cos (\frac{2 π}{7}) + cos (\frac{2 π}{7}) . cos (\frac{π}{7})$ $cos ((2pi)/7) + cos ((2pi)/7).cos ((pi)/7)$ =

$= cos (\frac{2 π}{7}) (1 + cos (\frac{π}{7}))$ $= cos ((2pi)/7)(1 + cos ((pi)/7))$

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

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