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

Ex 2.2, 17 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 2


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

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.