Ex 2.1, 12 - Chapter 2 Class 12 Inverse Trigonometric Functions

Transcript

Ex 2.1, 12 Find the value of cos-1 (1/2) + 2 sin-1 (1/2) Solving cos-1 ( / ) Let y = cos-1 (1/2) cos y = (1/2) cos y = cos ( /3). Range of principal value of cos-1 is [0 , ] Hence, the principal value is /3. Solving sin-1 ( / ) Let y = sin-1 (1/2) sin y = 1/2 sin y = sin ( /6) Range of principal value of sin 1 is [( )/2 , /2 ] Hence, the principal value is /6 Now we have cos-1 1/2 = /3 & sin-1 1/2 = /6 Solving cos-1 1/2 + 2sin-1 1/2 = /3 + 2 /6 = /3 + /3 = ( + )/3 = 2 /3