The number of values of x where the function fx - 2 cos 3x - cos -3x attains its maximum- is

We have, f(x) = 2(cos 3x + cos √(3)x) = 4 cos ( 3+√(3)/2 ) x cos ( 3 √(3)/2 ) x ⩽ 4 and it is equal to 4 when both cos ( 3+√(3)/2 ) x and cos ( 3 √(3)/2 ) ...

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Standard XI

Mathematics

Use of Monotonicity for Proving Inequalities

The number of...

Question

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

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Solution

The correct option is A
1

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

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