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

• A. \((a+b)^2\)
• B. \((a-b)^2\)
• C. \(2\sqrt{a^2+b^2}\)
• D. \(2\sqrt{a^2-b^2}\)

Hint:

For expressions involving \(\sqrt A+\sqrt B\), square first. Then use identities such as \(\sin^2\theta\cos^2\theta=\frac14\sin^22\theta\) to determine extrema.

Answer 1

The Correct Option is B