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    Question

    If x = 4 cos A + 5 sin A snd y = 4 sin A – 5 cos

    A, then the value of x2+y2 is :
    A 25 Correct Answer Incorrect Answer
    B 41 Correct Answer Incorrect Answer
    D 16 Correct Answer Incorrect Answer

    Solution

    X = 4 cos A + 5 sin A y = 4 sin A − 5 cos A x 2 + y2 = (4 cos A + 5 sin A)2 + (4 sin A − 5 cos A)2 ((a + b)2 = a2 + b2 + 2ab) = (16cos2A+25sin2A +40 cos Asin A)+(16 sin2A +25cos2A− 40cosA sin A )2 (sin2A+ cos2A=1) =16+25=41

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