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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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