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      Question

      What is the simplified value of the given

      expression? 2(sin² 40° + sin² 50°) + 4sin 30° - (2sec 60° + cot 45°)
      A 1 Correct Answer Incorrect Answer
      C 2 Correct Answer Incorrect Answer
      D -1 Correct Answer Incorrect Answer

      Solution

      2(sin ² 40° + sin ² 50°) + 4sin 30° - (2sec 60° + cot 45°)
      Using, sin(90° - A) = cos A
      = 2{sin ² 40° + sin ² (90 - 40)°} + 4 x 1/2 - {2 x 2 + 1}
      = 2(sin ² 40° + cos ² 40°) + 2 - (4 + 1)
      Using, sin ² A + cos ² A = 1
      = 2 x 1 + 2 - 5 = 2 + 2 - 5 = -1

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