Question

Let \(f(x)=2\sqrt{\,2\sin x+2\sqrt{2}\cos x\,},\; x\in\mathbb{R}\). Then the value of \(f\!\left(\frac{\pi}{12}\right)\) is equal to

• A. \(\sqrt{3}\)
• B. \(2\sqrt{3}\)
• C. \(\frac{\sqrt{3}}{2}\)
• D. \(\sqrt{2}\)
• E. \(2\sqrt{2}\)

Hint:

Converting the form \((\sin x + \cos x)\) to \(\sqrt{2} \sin(x + 45^\circ)\) is often much faster than trying to calculate values for unusual angles like \(15^\circ\) directly.

Answer 1

The Correct Option is B