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

Misc. 2 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 2

  1. Chapter 2 Class 12 Inverse Trigonometric Functions (Term 1)
  2. Serial order wise

Transcript

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°) But, range of 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 (𝜋/6) Hence, y = 𝝅/𝟔 Which is in the range of tan-1 i.e. ((−π)/2, π/2) Hence, tan–1(𝐭𝐚𝐧⁡〖𝟑𝛑/𝟒〗 ) = y = 𝝅/𝟔 (As tan (180 + θ) = tan θ)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.