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      Question

      sin2 7 ° + sin2 8 ° +

      sin2 9 ° + sin2 10 ° + ……… + sin2 83 ° = ?
      A 43.5 Correct Answer Incorrect Answer
      B 38.5 Correct Answer Incorrect Answer
      C 40.5 Correct Answer Incorrect Answer
      D 44.4 Correct Answer Incorrect Answer

      Solution

      sin2 7 ° + sin2 8 ° + sin2 9 ° + sin2 10 ° + ……… + sin2 83 ° = (sin 2 7 ° + sin2 83 °)+(sin2 8 ° + sin2 82 °) + .…. + (sin2 44 ° + sin2 46 °) + sin2 45 ° = (sin2 7 ° + cos2 7 °)+(sin2 8 °+ cos2 8 °) + .…. + (sin2 44 ° + cos2 44 °)+ sin2 45 °  {As sin (90 ° - θ) = cos θ} = (1)+(1) + .…. upto 38 times + sin2 45 ° { As sin2 θ + cos2 θ= 1} = 38 + sin2 45 °                                  = 38 + (1/√2)2  {As sin 45 ° =1/√2 } = 38 +   = 38.5

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