Ex 2.2, 17 - Find tan-1(tan 3pi/4) - Chapter 2 Class 12 Inverse - Finding pricipal value

  1. Chapter 2 Class 12 Inverse Trigonometric Functions
  2. Serial order wise
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Ex 2.2, 17 Find the values of tan-1(tan⁡〖3π/4〗 ) Let y = tan-1(tan⁡〖3π/4〗 ) tan y =〖 tan〗⁡〖3π/4〗 tan y = tan (135°) We know that range of principal value of tan-1 is (− 𝜋/2 , 𝜋/2 ) i.e. (− 90° ,90°) Hence y = 135° not possible Now, tan y = tan (135°) tan y = tan (180° – 45°) tan y = – tan (45°) tan y = tan (– 45°) tan y = tan (–45 × 𝜋/180) tan y = tan ((− 𝜋)/4) y = (− 𝜋)/4 Which is in the range of principal value of tan-1 i.e. ((−π)/2, π/2) Hence, tan-1 (tan⁡〖3π/4〗 ) = y = (− 𝜋)/4

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