How do you use the half angle formula to simplify ${cos}^{2} (\frac{π}{3})$ $cos^2(pi/3)$ ?

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Answer 1 · 2015-05-17T15:06:42

Use trig identity: $2 {cos}^{2} a = 1 + cos 2 a .$ $2cos^2 a = 1 + cos 2a.$

#2cos^2 (pi/3) = 1 + cos (2pi)/3

Trig table gives $cos (\frac{2 π}{3}) = - \frac{1}{2}$ $cos ((2pi)/3) = -1/2$

${cos}^{2} (\frac{π}{3}) = 1 - \frac{1}{2} = \frac{1}{2}$ $cos^2 (pi/3) = 1 - 1/2 = 1/2$

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