Ex 2.2, 21 - Find: tan-1 root 3 - cot-1 (- root 3) - Finding pricipal value

  1. Chapter 2 Class 12 Inverse Trigonometric Functions
  2. Serial order wise
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Ex 2.2, 21 Find value of : tan-1 √3 – cot-1 (−√3) Finding tan-1 √𝟑 Let y = tan-1 √3 tan y = √3 tan y = tan (π/3) We know that principal value range of tan-1 is ((− π)/2,π/2) Hence, principal value of tan-1 √3 is π/3 ∴ tan-1 √3 = π/3 Finding cot-1 (−√𝟑) Let x = cot-1 (−√3) cot x = – √3 cot x = cot 5π/6 Range of principal value of cot−1 is (0,π) Hence, principal value is 5π/6 ∴ cot-1 (−√3) = 5π/6 Hence, tan-1 √3 = π/3 & cot-1 (−√3) = 5π/6 Now calculating tan-1 √3 – cot-1 (−√3) = π/3 − 5π/6 = (2𝜋 − 5π)/6 = (−3π)/6 = (−π)/2 Hence option (B) is correct

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