In a $\Delta ABC$,the value of $\sin A \cos B \cos C + \sin B \cos C \cos A + \sin C \cos A \cos B$ is

The range of $f(x) = \cos x - \sin x$ is

Let $f(x) = \cos 5x + A \cos 4x + B \cos 3x + C \cos 2x + D \cos x + E$,and $T = f(0) - f\left(\frac{\pi}{5}\right) + f\left(\frac{2\pi}{5}\right) - f\left(\frac{3\pi}{5}\right) + \dots + f\left(\frac{8\pi}{5}\right) - f\left(\frac{9\pi}{5}\right)$. Then,$T$

If the extreme values of the function $f(x)=(2 \sqrt{6}+1) \cos x+(2 \sqrt{2}-\sqrt{3}) \sin x-6$ are $m$ and $M$,then $\sqrt{|M^2-m^2|}=$

The least value of $(\cos^{2}\theta - 6\sin\theta \cos\theta + 3\sin^{2}\theta + 2)$ is:

The number of integral values of $k$,for which the equation $7 \cos x + 5 \sin x = 2k + 1$ has a solution,is