1 - cos^2 x + 2 cos x = -2 then move everything to the right
0 =cos^2 x - 2 cos x - 3
Factor (cos x - 3)(cos x + 1) = 0 and since cos x can't be 3 (it's always between -1 and 1 inclusive), you know the only answer is when cos x = -1, which is at x = π
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sin^2 x = 1 - cos^2 x so sub that into make it
1 - cos^2 x + 2 cos x = -2 then move everything to the right
0 =cos^2 x - 2 cos x - 3
Factor (cos x - 3)(cos x + 1) = 0 and since cos x can't be 3 (it's always between -1 and 1 inclusive), you know the only answer is when cos x = -1, which is at x = π