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NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

The value of 2 sin - 1 ⁡ 4 5 + 2 sin - 1 ⁡ 5 13 + 2 sin - 1 ⁡ 16 65 is equal to

Options

  1. A3 π 2
  2. Bπ 2
  3. Cπ
  4. D2 π

Correct answer

C. π

Step-by-step solution

2 sin - 1 ⁡ 4 5 + sin - 1 ⁡ 5 13 + sin - 1 ⁡ 16 65 = 2 sin - 1 ⁡ 4 5 1 - 5 13 2 + 5 13 1 - 4 5 2 + 2 sin - 1 ⁡ 16 65 = 2 sin - 1 ⁡ 48 65 + 15 65 + 2 sin - 1 ⁡ 16 65 = 2 sin - 1 ⁡ 63 65 + sin - 1 ⁡ 16 65 = 2 cos - 1 ⁡ 16 65 + sin - 1 ⁡ 16 65   ∵ sin - 1 ⁡ x = cos - 1 ⁡ 1 - x 2 = π

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