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Ex 2.1, 12 - Find value of cos-1 (1/2) + 2 sin-1 (1/2) - Finding pricipal value

  1. Chapter 2 Class 12 Inverse Trigonometric Functions
  2. Serial order wise
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Ex 2.1, 12 Find the value of cos-1 (1/2) + 2 sin-1 (1/2) Solving cos-1 (𝟏/𝟐) Let y = cos-1 (1/2) cos y = (1/2) cos y = cos (π/3). Range of principal value of cos-1 is [0 , 𝜋] Hence, the principal value is π/3. Solving sin-1 (𝟏/𝟐) Let y = sin-1 (1/2) sin y = 1/2 sin y = sin (π/6) Range of principal value of sin −1 is [(−𝜋)/2 , 𝜋/2 ] Hence, the principal value is π/6 Now we have cos-1 1/2 = 𝜋/3 & sin-1 1/2 = 𝜋/6 Solving cos-1 1/2 + 2sin-1 1/2 = 𝜋/3 + 2 × 𝜋/6 = 𝜋/3 + 𝜋/3 = (𝜋 + 𝜋)/3 = 2𝜋/3

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