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Ex 2.1, 11 - Find value tan-1 (1) + cos-1 (-1/2) + 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, 11 Find the value of tan-1 (1) + cos-1 (−1/2) + sin-1 (−1/2) Solving tan−1 (1) Let y = tan−1 (1) tan y = 1 tan y = tan (π/4) Range of principal value of tan−1 is (−π/2,π/2) Hence, the principal value of  tan-1 (1) is π/4 Solving cos-1 (−𝟏/𝟐) Let y = cos-1 (−1/2) cos y = −1/2 cos y = cos (2π/3) Range of principal value of cos-1 is [0 , 𝜋] Hence, the principal value is 2π/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 between [(−𝜋)/2 , 𝜋/2] Hence, the principal value is (−π)/6 Now we have tan-1 (1) = π/4 , cos-1(−1/2) = 2π/3 , sin-1 (−1/2) = (−π)/6 Finding tan-1 (1) + cos-1 ((−1)/2) + sin-1 ((−1)/2) = π/4 + 2π/3 – π/6 = (3 × π + 4 × (2π) − 2 (π))/12 = (3π + 8π − 2π)/12 = 9π/12 = 3π/4

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