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Misc 2 - Find tan-1 (tan 7pi/6) - Chapter 2 Inverse CBSE - Miscellaneous

  1. Class 12
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Misc 2 Find the value of  tan-1(tan⁡〖7π/6〗 ) Let y = tan-1(tan⁡〖7π/6〗 ) tan y =〖 tan〗⁡〖7π/6〗 tan y = tan (210°) We know that range of principal value of tan-1 is (− 𝜋/2 , 𝜋/2 ) i.e. (− 90° ,90°) Hence y = 210° not possible Now, tan y = tan (210°) tan y = tan (180° + 30°) tan y = tan (30°) tan y = tan (30 × 𝜋/180) tan y = tan (𝜋/6) Hence, y = 𝜋/6 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/𝟔

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