If x=p\sin A\cos B, y=p\sin A\sin B and z=p\cos A, then what is the value of x^{2}+y^{2}+z^{2}?

Explanation

Sum of squares: x^2 + y^2 = p^2\sin^2 A\cos^2 B + p^2\sin^2 A\sin^2 B = p^2\sin^2 A(\cos^2 B + \sin^2 B) = p^2\sin^2 A. Then x^2 + y^2 + z^2 = p^2\sin^2 A + p^2\cos^2 A = p^2(\sin^2 A + \cos^2 A) = p^2.

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