First take a look at the problem :
Find the minimum value of the trigonometrical function :
If we proceed by perfect-square method , we get ,
But this minimum value will be achieved if and only if ,
which when solved gives ( approximately ) , which is certainly not possible since maximum value of is 1
Does this mean that the function does not have any minimum value .
But if we plot the graph of , it looks like it has a minimum value of 13 .
Please analyze and explain !