NTA Abhyas JEE Main2020MathematicsFunctionsPractice

The number of real solutions of cot - 1 ⁡ x x + 3 + sin - 1 ⁡ x 2 + 3 x + 1 = π 2 is/are

Options

A0
B1
C2
DInfinite

Correct answer

A. 0

Step-by-step solution

Let, f x = cot - 1 ⁡ x x + 3 + sin - 1 ⁡ x 2 + 3 x + 1 For f x to be defined, we have x 2 + 3 x ≥ 0 and 0 ≤ x 2 + 3 x + 1 ≤ 1 Which is only possible if x 2 + 3 x = 0 ⇒ x = 0 , - 3 But these values do not satisfy the equation ∴ Number of solutions = 0

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