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    Question

    Find the value of the following:sin(36° + A) ×

    cos(54° – A) + cos(36° + A) × sin(54°–A)
    A 1/2 Correct Answer Incorrect Answer
    C 1 Correct Answer Incorrect Answer
    D √3/2 Correct Answer Incorrect Answer

    Solution

    sin(36° + A) × cos(54° – A) + cos(36° + A) × sin(54°–A)

    We know that, sin(X + Y) = sinX × cos Y + cosX × sinY

    Similarly, sin(36° + A) × cos(54° – A) + cos(36° + A) × sin(54°–A) = sin{(36 o  + A) + (54 o  – A)}

    = sin(36 o  + A + 54 o  – A) = sin90 o  = 1

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