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      Question

      What is the simplified value of the given

      expression? 4(sin² 20° + sin² 70°) + 2sin 30° - (2sec 60° + cot 45°)
      A 1 Correct Answer Incorrect Answer
      C 3 Correct Answer Incorrect Answer
      D -1 Correct Answer Incorrect Answer

      Solution

      4(sin ² 20° + sin ² 70°) + 2sin 30° - (2sec 60° + cot 45°)
      Using, sin(90° - A) = cos A
      = 4{sin ² 20° + sin ² (90 - 20)°} + 2 x 1/2 - {2 x 2 + 1}
      = 4(sin ² 20° + cos ² 20°) + 1 – 5
      Using, sin ² A + cos ² A = 1
      = 4 x 1 + 1 - 5 = 4 + 1 - 5 = 0

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