HMMT 2001 T5

Find all $x$ between $-\frac{\pi}{2}$ and $\frac{\pi}{2}$ such that $1-\sin ^{4} x-\cos ^{2} x=\frac{1}{16}$ .

Dataset text NuminaMath olympiads. Quoted with source.

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x= \pm \frac{\pi}{12}, \pm \frac{5 \pi}{12}

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