How do you evaluate this $cos (\frac{2 π}{7}) \cdot cos (\frac{3 π}{7}) \cdot cos (\frac{6 π}{7})$ $cos((2pi)/7)cos((3pi)/7)cos((6pi)/7)$ ?

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How do you evaluate this $cos (\frac{2 π}{7}) \cdot cos (\frac{3 π}{7}) \cdot cos (\frac{6 π}{7})$ $cos((2pi)/7)cos((3pi)/7)cos((6pi)/7)$ ?

Please, explain me EVERYTHING, I am pretty awful at trigonometry

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Answer 1 · 2017-03-22T21:14:06

$cos (\frac{2 π}{7}) \cdot cos (\frac{3 π}{7}) \cdot cos (\frac{6 π}{7})$ $cos((2pi)/7)*cos((3pi)/7)*cos((6pi)/7)$

$= \frac{1}{8 sin (\frac{2 π}{7})} \cdot 4 \cdot 2 sin (\frac{2 π}{7}) cos (\frac{2 π}{7}) \cdot cos (\frac{3 π}{7}) \cdot cos (\frac{6 π}{7})$ $=1/(8sin((2pi)/7))*4*2sin((2pi)/7)cos((2pi)/7)*cos((3pi)/7)*cos((6pi)/7)$

$= \frac{1}{8 sin (\frac{2 π}{7})} \cdot 2 \cdot 2 sin (\frac{4 π}{7}) \cdot cos (\frac{3 π}{7}) \cdot cos (\frac{6 π}{7})$ $=1/(8sin((2pi)/7))*2*2sin((4pi)/7)*cos((3pi)/7)*cos((6pi)/7)$

$= \frac{1}{8 sin (\frac{2 π}{7})} \cdot 2 \cdot 2 sin (π - \frac{3 π}{7}) \cdot cos (\frac{3 π}{7}) \cdot cos (\frac{6 π}{7})$ $=1/(8sin((2pi)/7))*2*2sin(pi-(3pi)/7)*cos((3pi)/7)*cos((6pi)/7)$

$= \frac{1}{8 sin (\frac{2 π}{7})} \cdot 2 \cdot 2 sin (\frac{3 π}{7}) \cdot cos (\frac{3 π}{7}) \cdot cos (\frac{6 π}{7})$ $=1/(8sin((2pi)/7))*2*2sin((3pi)/7)*cos((3pi)/7)*cos((6pi)/7)$

$= \frac{1}{8 sin (\frac{2 π}{7})} \cdot 2 sin (\frac{6 π}{7}) \cdot cos (\frac{6 π}{7})$ $=1/(8sin((2pi)/7))*2sin((6pi)/7)*cos((6pi)/7)$

$= \frac{1}{8 sin (\frac{2 π}{7})} sin (\frac{12 π}{7})$ $=1/(8sin((2pi)/7))sin((12pi)/7)$

$= \frac{1}{8 sin (\frac{2 π}{7})} sin (2 π - \frac{2 π}{7})$ $=1/(8sin((2pi)/7))sin(2pi-(2pi)/7)$

$= \frac{1}{8 sin (\frac{2 π}{7})} (- sin (\frac{2 π}{7}))$ $=1/(8sin((2pi)/7))(-sin((2pi)/7))$

$= - \frac{1}{8}$ $=-1/8$

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How do you evaluate this $cos (\frac{2 π}{7}) \cdot cos (\frac{3 π}{7}) \cdot cos (\frac{6 π}{7})$ $cos((2pi)/7)cos((3pi)/7)cos((6pi)/7)$ ?

Please, explain me EVERYTHING, I am pretty awful at trigonometry

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Please, explain me EVERYTHING, I am pretty awful at trigonometry

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