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      Question

      Find the value of the given trigonometric

      expression: (sin 25°cos 65° + cos²25°) × sin 30° + (cos 60°tan 45°) × sec 60°
      A 1/2 Correct Answer Incorrect Answer
      B 5/2 Correct Answer Incorrect Answer
      C 2 Correct Answer Incorrect Answer
      D 3/2 Correct Answer Incorrect Answer

      Solution

      (sin 25°cos 65° + cos²25°) × sin 30° + (cos 60°tan 45°) × sec 60° = {sin 25°cos (90° – 25°) + cos²25°} × sin 30° + cos 60°tan 45°sec 60° Using, cos (90° – A) = sin A = (sin²25° + cos²25°) sin 30° + cos 60°tan45°sec 60° Using, sin²A + cos²A = 1 = {1 × (1/2)} + {(1/2) × 1 × 2} = (1/2) + 1 = (3/2) Hence, option D.

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