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 :

Question

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 :

${\left( {a - b} \right)^2}$

$2\sqrt {{a^2} + {b^2}} $

${\left( {a + b} \right)^2}$

$2\left( {{a^2} + {b^2}} \right)$

Solution

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