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NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

The value of sin - 1 ⁡ sin ⁡ 17 + cos - 1 ⁡ cos ⁡ 10 is equal to

Options

  1. A27
  2. B- 27
  3. C17 - 5 π
  4. D9 π - 27

Correct answer

D. 9 π - 27

Step-by-step solution

sin - 1 ⁡ sin ⁡ 17 = sin - 1 ⁡ sin ⁡ 17 - 5 π + 5 π = 5 π - 17 cos - 1 ⁡ cos ⁡ 10 = cos - 1 ⁡ cos ⁡ 10 - 3 π + 3 π = cos - 1 ⁡ cos ⁡ 3 π + 10 - 3 π = cos - 1 ⁡ - cos ⁡ 10 - 3 π = π - cos - 1 ⁡ cos ⁡ 10 - 3 π = π - 10 - 3 π = 4 π - 10 Hence, sin - 1 ⁡ sin ⁡ 17 + cos - 1 ⁡ cos ⁡ 10 = 9 π - 27

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