The number of distinct real roots of the equation, $$\left| {\matrix{ {\cos x} & {\sin x} & {\sin x} \cr {\sin x} & {\cos x} & {\sin x} \cr {\sin x} & {\sin x} & {\cos x} \cr } } \right| = 0$ in the interval $\left[ { - {\pi \over 4},{\pi \over 4}} \right]$$ is :

Question

The number of distinct real roots of the equation,

$$\left| {\matrix{ {\cos x} & {\sin x} & {\sin x} \cr {\sin x} & {\cos x} & {\sin x} \cr {\sin x} & {\sin x} & {\cos x} \cr } } \right| = 0$ in the interval $\left[ { - {\pi \over 4},{\pi \over 4}} \right]$$ is :

Solution

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