Question

If $x=r\cos \alpha \cos \beta$ and $y=r\cos \alpha \sin \beta$, $z=r$ $\sin \alpha$ then $x^2+y^2+z^2$ is equal to

• A. $r^2$
• B. $r^4$
• C. 1
• D. None of these

Answer 1

The correct option is A $r^2$

$x^2+y^2+z^2=r^2\left({\cos }^2\alpha \right)({\cos }^2\beta +{\sin }^2\beta )+r^2{\sin }^2\alpha$
$=r^2{\cos }^2\alpha +r^2{\sin }^2\alpha$
$=r^2({\cos }^2\alpha +{\sin }^2\alpha )=r^2$