Question -12

Geometry Level 4

How many distinct real roots xx satisfy the determinant

sinxcosxcosxcosxsinxcosxcosxcosxsinx=0 \left | \begin{array}{ccc} \sin x & \cos x & \cos x\\ \cos x& \sin x & \cos x\\ \cos x & \cos x& \sin x \\ \end{array} \right |=0 lie in the interval [π4,π4][-\frac{\pi}{4},\frac{\pi}{4}] ?


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