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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°) 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

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.