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NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

The value of 2 cos - 1 ⁡ 2 3 - 2 cos - 1 ⁡ 6 + 1 2 3 is equal to

Options

  1. Aπ 3
  2. Bπ 4
  3. Cπ 2
  4. Dπ 6

Correct answer

A. π 3

Step-by-step solution

2 c o s - 1 2 3 - 2 c o s - 1 6 + 1 2 3 = 2 t a n - 1 1 2 - 2 t a n - 1 3 - 2 1 + 6 = 2 t a n - 1 1 2 - 2 t a n - 1 3 - t a n - 1 2 = 2 t a n - 1 1 2 + t a n - 1 2 - 2 tan - 1 ⁡ 3 = π - 2 π 3 = π 3

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