Ex 2.2, 11 - Chapter 2 Class 12 Inverse Trigonometric Functions
Last updated at Dec. 16, 2024 by Teachoo
Finding principal value
Principal Value
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Chapter 2 Class 12 Inverse Trigonometric Functions
Concept wise
Transcript
Ex 2.2, 11 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
