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      Question

      What is the simplified value of the given

      expression? 3(sin² 50° + sin² 40°) + 6sin 30° - (3sec 60° + cot 45°)
      A 1 Correct Answer Incorrect Answer
      C 2 Correct Answer Incorrect Answer
      D -1 Correct Answer Incorrect Answer

      Solution

      3(sin ² 50° + sin ² 40°) + 6sin 30° - (3sec 60° + cot 45°)
      Using, sin(90° - A) = cos A
      = 3{sin ² 50° + sin ² (90 - 50)°} + 6 x 1/2 - {3 x 2 + 1}
      = 3(sin ² 50° + cos ² 50°) + 3 - 7
      Using, sin ² A + cos ² A = 1
      = 3 x 1 + 3 - 7 = 3 + 3 - 7 = -1

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