Factor the first equation: cos^2 x - cos x - 2 = (cos x - 2)(cos x + 1) = 0.
Since -1 <= cos x <= 1, the first factor is not 0, and cos x + 1 = 0.
From cos x = - 1 we get x = pi + 2*pi*n (n is any integer).
The second equation can be solved as follows: 4 sin^2 x + 2 = 3; 4 sin^2 x = 1; sin^2 x = 1/4; sinx = +/- 1/2,
and x = +/- pi/6 + pi*n (n is any integer).
If you add the restriction 0 < x < 2 pi,
then the first equation has only one solution, x = pi;
the second equation has four solutions: x = pi/6, x=5*pi/6, x = 7*pi/6, and x = 11*pi/6.
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