Ex 3.3, 2 - Prove 2 sin2 pi/6 + cosec2 7pi/6 cos2 pi/3 =  3/2 - Finding Value of trignometric functions, given angle

 

 

 

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise
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E 3.3, 2 Prove that 2sin2 /6 + cosec2 7 /6 cos2 /3 = 3/2 Taking L.H.S 2sin2 /6 + cosec2 7 /6 cos2 /3 Putting = 180 = 2 sin2 180/6 + cosec2 (7 180)/6 cos2 180/3 = 2sin2 30 + cosec2 210 cos2 60 = 2(sin 30 )2 + ( cosec 210 )2 (sin 60 )2 Here, sin 30 = 1/2 sin 60 = 3/2 For cosec 210 , lets first calculate sin 210 sin 210 = sin (180 + 30 ) = - sin 30 = ( 1)/2 So, cosec 210 = 1/sin 210 = 1/(( 1)/2) = 2/( 1 ) = 2 Putting the value = 2(sin 30 )2 + ( cosec 210 )2 (sin 60 )2 = 2 (1/2)^2 + ( 2)2 (1/2)^2 = 2 1/4 + 4 1/4 = 1/2 + 1 = (1 + 2)/2 = 3/2 = R.H.S Hence proved

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