Ex 2.2, 19 - Find cos-1(cos 7pi/6) is equal to (A) 7pi/6 - Finding pricipal value

  1. Chapter 2 Class 12 Inverse Trigonometric Functions
  2. Serial order wise
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Ex 2.2, 19 Find the values of cos-1(cos 7π/6)  is equal to (A) 7π/6 (B) 5𝜋/6 (C) 𝜋/3 (D) 𝜋/6 Let y = cos −1 (cos 7π/6) cos y = cos (7π/6) cos y = cos (210°) We know that range of principal value of cos is [0,π] i.e. [0° ,180°] Hence y = 210° not possible Now, cos y = cos (210°) cos y = cos (360° – 150°) cos y = cos (150°) cos y = cos (150 × 𝜋/180) cos y = cos (5𝜋/6) y = 5𝜋/6 Which is in the range of principal value of cos-1 i.e. [0,π] Hence , cos −1 (cos 7π/6) = y = 5𝜋/6 Thus, option (B) is correct

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