Given $$A = {\sin ^2}\theta + {\cos ^4}\theta $$ then for all real values of $$\theta $$

Find the real values of x and y for which the following equation is satisfied $$\,{{(1 + i)x - 2i} \over {3 + i}} + {{(2 + 3i)y + i} \over {3 - i}} = i$$

For all $$\theta $$ in $$\left[ {0,\,\pi /2} \right]$$ show that, $$\cos \left( {\sin \theta } \right) \ge \,\sin \,\left( {\cos \theta } \right).$$

Let $$y = \sqrt {{{\left( {x + 1} \right)\left( {x - 3} \right)} \over {\left( {x - 2} \right)}}} $$

Find all the real values of $$x,$$ for which $$y$$ takes real values.