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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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E𝑥3.3, 2 Prove that 2sin2 π/6 + cosec2 7π/6 cos2 π/3 = 3/2 Taking L.H.S 2sin2 π/6 + cosec2 7π/6 cos2 π/3 Putting π = 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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