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Given cos x = cos α, all possible x are

Ax = nπ + (−1)^n α, n ∈ Z
Bx = nπ + α, n ∈ Z
Cx = nπ ± α, n ∈ Z
Dx = 2nπ ± α, n ∈ Z
Answer & Solution
Correct answer: D. x = 2nπ ± α, n ∈ Z
cos x − cos α = 0 gives a sine factor that vanishes for x = 2nπ ± α.
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