If x = r cos sin, y = r cos cos and z = r sin , show that x² +y² +z² = r².
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Hello, This is pretty simple ! $\displaystyle x^2+y^2+z^2=r^2[\cos^2\alpha\sin^2\beta+\cos^2\alpha\cos^2\beta+\s in^2\alpha]=r^2[\cos^2\alpha(\sin^2\beta+\cos^2\beta)+\sin^2\alpha]$ $\displaystyle =r^2[\cos^2\alpha+\sin^2\alpha]=r^2$
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