Finding principal value
Example 1 Important
Ex 2.1, 1
Ex 2.1, 3
Ex 2.1, 10 Important
Ex 2.1, 2
Ex 2.1, 5 Important
Ex 2.1, 9
Ex 2.1, 7 Important
Ex 2.1, 4 Important
Ex 2.1, 6
Ex 2.1, 8 Important
Example 2
Ex 2.2, 10
Example 6 Important
Ex 2.2, 8
Ex 2.2, 11 You are here
Misc 2 Important
Ex 2.2, 13 (MCQ) Important
Misc 1
Ex 2.2, 14 (MCQ) Important
Ex 2.2, 15 (MCQ)
Ex 2.1, 12 Important
Ex 2.1, 14 (MCQ) Important
Ex 2.1, 11 Important
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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 (As tan (180 – θ) = – tan θ) (tan (–θ) = – tan θ)
