How do you solve $cos(2theta)+cos(theta)=0$ ?

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Answer 1 · 2015-06-08T05:05:31

Use trig identity: $cos 2a = 2cos^2 a - 1.$

$2cos^2 x + cos x - 1 = 0.$

Call cos x = t, solve the quadratic equation: y = 2t^2 + t - 1 = 0

Since a - b + c = 0, use shortcut. One real root is t = -1 and the other is $(-c/a = 1/2.)$

a. cos x = t = -1 --> $x = pi$

b. $cos x = t = 1/2 --> x = +- pi/3$

How do you solve cos(2theta)+cos(theta)=0cos(2theta)+cos(theta)=0?