If $x = r sin A cos C, y = r sin A sin C$ and $z = r cos A$ , then $r^{2} = x^{2} + y^{2} + z^{2}$

True

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False

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Solution

The correct option is A True
$x^{2} + y^{2} + z^{2}$
$= r^{2} {sin}^{2} A {cos}^{2} C + r^{2} {sin}^{2} A {sin}^{2} C + r^{2} {cos}^{2} A$
$= r^{2} {sin}^{2} A ({cos}^{2} C + {sin}^{2} C) + r^{2} {cos}^{2} A$
$= r^{2} {sin}^{2} A + r^{2} {cos}^{2} A$
$= r^{2} ({sin}^{2} A + {cos}^{2} A)$
$= r^{2}$

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