This question can be solved by using AM>=GM.
i JUST WANT TO KNOW THAT IN WHICH TYPE OF QUESTIONS SHOULD WE USE THIS CONCEPT?
1well you can see clearly that multiplying both the terms simplify matters ..
this is usually the first step. In more complicated problems this will not be so directly visible.
There are quite a few nice threads on inequalities in this forum.
you will want to check them out
1do we also come asross questions where we have to use GM>=HM or AM>=HM
11Obviously A.M-G.M simplifies this further....because the product being constant, the minima will be achieved only when both the terms are equal.
So that gives θ=Π4, from which b) follows.