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2sin2 x

2(1 - cos2 x) = 2 + cos x

2 - 2cos2 x = 2 + cos x

- 2cos2 x - cos x = 0

cos x(-cos x - 1) = 0

cos x = 0 or -cos x - 1 = 0

cos x = -1

Since the cosine has a period of 2pi, in the interval 0 ≤ x ≤ 2pi

when cos x = 0, x = pi/2 and x = 3pi/2, and

when cos x = -1, x = pi.

All values of x that satisfy the given equation are:

x = pi/2 + 2npi, x = pi +2npi, and x = 3pi/2+ 2npi where n is any integer.

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Q: What is the work for 2 sin squared x equals 2 plus cos x?
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