NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

The number of real solutions of cot - 1 ⁡ x x + 4 + cos - 1 ⁡ x 2 + 4 x + 1 = π 2 is equal to

Options

A0
B1
C2
DInfinite

Correct answer

C. 2

Step-by-step solution

Let, f x = cot - 1 ⁡ x x + 4 + cos - 1 ⁡ x 2 + 4 x + 1 For f x to be defined, we have x 2 + 4 x ≥ 0 and 0 ≤ x 2 + 4 x + 1 ≤ 1 Which is only possible if x 2 + 4 x = 0 ⇒ x = 0 , - 4 Also these values satisfies the equation ∴ Number of solutions = 2

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