question_answer

If\[u=\sqrt{{{a}^{2}}{{\cos }^{2}}\theta +{{b}^{2}}{{\sin }^{2}}\theta }\] \[+\sqrt{{{a}^{2}}{{\sin }^{2}}\theta +{{b}^{2}}{{\cos }^{2}}\theta },\] then the difference between the maximum and minimum values of\[{{u}^{2}}\]is given by

A) \[2({{a}^{2}}+{{b}^{2}})\]  

B)        \[2\sqrt{{{a}^{2}}+{{b}^{2}}}\]  

C)        \[{{(a+b)}^{2}}\]          

D)        \[{{(a-b)}^{2}}\]

Correct Answer: D

Solution :

And        Now,