Verified answer

This is a quadratic equation, with cos(x) as the variable instead of the usual x:

2cos²(x) - cos(x) - 1 = 0.

This factors as

(2cos(x)+1)(cos(x)-1) = 0, so cos(x) = -1/2 or +1.

So, x = cosˉ¹(-1/2) = 2π/3 or 4π/3

or

x = cosˉ¹(1) = 2π.

(2cosx+1)(cosx-1) = 0

cos x = 1 or -1/2

For the interval 0<x<=2pi

x = 2pi/3, 4pi/3 and 2pi

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