If $$y = {\left( {\sin x} \right)^{\tan x}},$$ then $${{dy} \over {dx}}$$ is equal to

In a triangle $$ABC$$, $$AD$$ is the altitude from $$A$$. Given $$b>c$$, $$\angle C = {23^ \circ }$$ and $$AD = {{abc} \over {{b^2} - {c^2}}}$$ then $$\angle B = $$.................

A circle is inscribed in an equilateral triangle of side $$a$$. The area of any square inscribed in this circle is ..............

If the lengths of the sides of triangle are $$3, 5, 7$$ then the largest angle of the triangle is