The approximate value of $\cos \left(59^{\circ} 30^{\prime}\right)$ is (given $1^{\circ}=0.0175^{\mathrm{c}}, \sin 60^{\circ}=0.8660$ )

The value of $\sqrt{3} \cot 20^{\circ}-4 \cos 20^{\circ}$ is equal to

If $A+B=\frac{\pi}{2}$ then the maximum value of $\cos \mathrm{A} \cdot \cos \mathrm{B}$ is

If $\tan \mathrm{A}=\frac{1}{\sqrt{x\left(x^2+x+1\right)}}, \tan \mathrm{B}=\frac{\sqrt{x}}{\sqrt{x^2+x+1}}$ and $\tan \mathrm{C}=\sqrt{x^{-1}+x^{-2}+x^{-3}}$ then