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    Question

    If x = r sin A cos B, y = r sin A sin B and z = r cos A,

    then find x² + y² + z².
    A 2r² Correct Answer Incorrect Answer
    B 3/2 r² Correct Answer Incorrect Answer
    C r² Correct Answer Incorrect Answer
    D r²(cos² B + cos² A) Correct Answer Incorrect Answer

    Solution

    x = r sin A cos B, y = r sin A sin B z = r cos A Now, x² + y² + z² = (r sin A cos B) ² + (r sin A sin B) ² + (r cos A)2 = r2 sin2 A (cos² B + sin² B) + r2 cos² A = r² sin² A + r2 cos² A = r² (sin² A + cos² A) = r2

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