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      Question

      In a triangle ABC, if 5∠A = 3∠B = 15∠C, then find the

      value of cosA + sin(C + 25 ° )
      A (√2 + 1)/2 Correct Answer Incorrect Answer
      B (√2 + 1)/4 Correct Answer Incorrect Answer
      C (√2 + 2)/2 Correct Answer Incorrect Answer
      D 1 Correct Answer Incorrect Answer

      Solution

      Given, 5∠A = 3∠B = 15∠C

      Or, ∠A:∠B:∠C = (1/5):(1/3):(1/15) = 3:5:1

      Let ∠A, ∠B and ∠C be '3x', '5x' and 'x', respectively

      Therefore, 3x + 5x + x = 180 o  (sum of the interior angles of a triangle is 180 o )

      Or, 9x = 180 o

      Or, x = 20 o

      Therefore, cosA + sin(C + 25 o ) = cos60 o  + sin45 o  = (1/2) + (1/√2) = {(√2 + 2)/2√2}

      Rationalising by multiplying numerator and denominator by √2, we get= (√2 + 1)/2

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