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If $A+B=C$,then the value of $\cos ^2 A+\cos ^2 B+\cos ^2 C-2 \cos A \cos B \cos C$ is equal to:

If $x \in (0, \frac{\pi}{4})$,then the expression $\frac{\cos x}{\sin^2 x(\cos x - \sin x)}$ cannot take which of the following values?

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The minimum value of $f(x) = a^{a^{x}} + a^{1-a^{x}}$,where $a, x \in R$ and $a > 0$,is equal to ..... .

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