The value of $$\tan ^{-1}\left(\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}\right), |x| < \frac{1}{2}, x \neq 0$$

If slope of a tangent to the curve $$x y+a x+b y=0$$ at the point $$(1,1)$$ on it is 2, then a - b is

The equation of a line, whose perpendicular distance from the origin is 7 units and the angle, which the perpendicular to the line from the origin makes, is $$120^{\circ}$$ with positive $$\mathrm{X}$$-axis, is

Let $$a, b, c$$ be the lengths of sides of triangle $$A B C$$ such that $$\frac{a+b}{7}=\frac{b+c}{8}=\frac{c+a}{9}=k$$. Then $$\frac{(\mathrm{A}(\triangle \mathrm{ABC}))^2}{\mathrm{k}^4}=$$