Question

The number of values of x where the function f(x) = 2 (cos 3x + cos $\sqrt{3x}$ attains its maximum, is

• A. 1
• B. 2
• C. 0
• D. Infinite

Answer 1

The correct option is A

1

We have,
$f\left(x\right)=2(cos3x+cos\sqrt{3}x)=4cos\left(\frac{3+\sqrt{3}}{2}\right)xcos\left(\frac{3-\sqrt{3}}{2}\right)x⩽4$
and it is equal to 4 when both cos $\left(\frac{3+\sqrt{3}}{2}\right)xandcos\left(\frac{3-\sqrt{3}}{2}\right)$
Are equal to 1 for a value of x. This is possible only when x = 0.
Hence (a) is the correct answer.