There exists a triangle $$ABC$$ satisfying the conditions

The principal value of $${\sin ^{ - 1}}\left( {\sin {{2\pi } \over 3}} \right)$$ is

If in a triangle $$ABC$$, $$\cos A\cos B + \sin A\sin B\sin C = 1,$$ Show that $$a:b:c = 1:1:\sqrt 2 $$

If the line $$ax+by+c=0$$ is a normal to the curve $$xy=1$$, then