Find all solutions of the equation in the interval $[0, 2 π)$ .
$\sin x = - \cos^{2} x - 1$
Write your answer in radians in terms of $π$ . If there is more than one solution, separate them with commas.
$x =$

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Answer

Thus, the final answer is $No Solution$ .

Steps

Step 1 ：Since $\sin x = \sqrt{1 - \cos^{2} x}$ , we get $- \sqrt{1 - \cos^{2} x} = - \cos^{2} x - 1$ .

Step 2 ：Squaring both sides, we get $1 - \cos^{2} x = \cos^{4} x + 2 \cos^{2} x + 1$ .

Step 3 ：Rearranging, we get $\cos^{4} x + 2 \cos^{2} x - \cos^{2} x + 2 = 0$ , which simplifies to $\cos^{4} x + \cos^{2} x + 2 = 0$ .

Step 4 ：This equation has no real solutions for $\cos x$ , so there are no solutions for $x$ in the given interval.

Step 5 ：Thus, the final answer is $No Solution$ .