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    Question

    If sin (2x + 50) o = cos (2y -

    50) o, such that, 0o < x + y < 90o, then find the value of tan(x + y) .
    A 1 Correct Answer Incorrect Answer
    C 1√3 Correct Answer Incorrect Answer
    D 1/√3 Correct Answer Incorrect Answer

    Solution

    Sin (2x + 50) o = cos(2y - 50) o

    We know that, sin Ao = cos (90 - A) o

    Or, cos {90o - (2x + 50) o} = cos(2y - 50) o

    Or, 90 - (2x + 50) = 2y - 50

    Or, 90 - 2x - 50 = 2y - 50

    Or, 2x + 2y = 90

    Or, 2 X (x + y) = 90

    So, x + y = (90/2) = 45o

    Therefore, tan (x + y) = tan 45o = 1

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