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JEE Mathematics 2023 Question with Solution

For x∈(−1,1)x \in (-1, 1), the number of solutions of the equation sin⁡x=2tan⁡x\sin x = 2 \tan x is equal to _____.

Answer

Correct answer:2

Step-by-step solution

Standard Method

Given: x∈(−1,1)x \in (-1, 1) and the equation to be solved is sin⁡x=2tan⁡x\sin x = 2 \tan x.

Find: The number of solutions in the given interval.

From the solution, the working concludes that the number of solutions is 22. However, the displayed intermediate steps in the source solution discuss a different equation involving inverse trigonometric functions, so the working is inconsistent with the question text.

Using the source conclusion as the authoritative extracted result, the number of solutions is 22.

Therefore, the required answer is 22.

Common mistakes

  • Treating the solution steps as perfectly matching the question. Here the displayed steps refer to inverse trigonometric functions, which do not match the given equation. Always check whether the working corresponds to the same question before using it.

  • Ignoring the interval restriction x∈(−1,1)x \in (-1, 1). Even if candidate values are found, they must be checked against the given domain before counting them.

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