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
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 You are here
Ex 2.1, 14 (MCQ) Important
Ex 2.1, 11 Important
Last updated at April 16, 2024 by Teachoo
Ex 2.1, 12 Find the value of cosโ1 (1/2) + 2 sinโ1 (1/2) Solving cosโ1 (๐/๐) Let y = cosโ1 (1/2) cos y = (1/2) cos y = cos (๐ /๐) โด y = ๐ /๐ Since Range of cosโ1 is [0 , ๐] Hence, the principal value is ๐ /๐ (Since cos ๐/3 = 1/2) Solving sinโ1 (๐/๐) Let y = sinโ1 (1/2) sin y = 1/2 sin y = sin (๐ /๐) โด y = ๐ /๐ Since Range of sinโ1 is [(โ๐)/2 " , " ๐/2] Hence, the Principal Value is ๐ /๐ (Since sin ๐/6 = 1/2) Now we have cosโ1 1/2 = ๐/3 & sinโ1 1/2 = ๐/6 Solving cosโ1 ๐/๐ + 2 sinโ1 ๐/๐ = ๐/3 + 2 ร ๐/6 = ๐/3 + ๐/3 = (๐ + ๐)/3 = ๐๐ /๐