Ex 2.1, 11 - Find value tan-1 (1) + cos-1 (-1/2) + sin-1 (-1/2) - Finding pricipal value

  1. Chapter 2 Class 12 Inverse Trigonometric Functions
  2. Serial order wise

Transcript

Ex 2.1, 11 Find the value of tan-1 (1) + cos-1 ( 1/2) + sin-1 ( 1/2) Solving tan 1 (1) Let y = tan 1 (1) tan y = 1 tan y = tan ( /4) Range of principal value of tan 1 is ( /2, /2) Hence, the principal value of tan-1 (1) is /4 Solving cos-1 ( / ) Let y = cos-1 ( 1/2) cos y = 1/2 cos y = cos (2 /3) Range of principal value of cos-1 is [0 , ] Hence, the principal value is 2 /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 between [( )/2 , /2] Hence, the principal value is ( )/6 Now we have tan-1 (1) = /4 , cos-1( 1/2) = 2 /3 , sin-1 ( 1/2) = ( )/6 Finding tan-1 (1) + cos-1 (( 1)/2) + sin-1 (( 1)/2) = /4 + 2 /3 /6 = (3 + 4 (2 ) 2 ( ))/12 = (3 + 8 2 )/12 = 9 /12 = 3 /4

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