Question

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

$x^2+y^2+z^2=r^2$

Answer 1

x =r cos A cos B => $x^2=r^{2}co{s}^{2}Aco{s}^{2}B$

y = r cos A sin B​​​​​​​ =>$y^2=r^{2}co{s}^{2}Asi{n}^{2}B$

z = r sin A => $z^2=r^{2}si{n}^{2}A$

=>$x^2+y^2+z^2=r^{2}co{s}^{2}Aco{s}^{2}B+r^{2}co{s}^{2}Asi{n}^{2}B+r^{2}si{n}^{2}A=r^2\left(co{s}^{2}A\right(co{s}^{2}B+si{n}^{2}B)+si{n}^{2}A)=r^2(si{n}^{2}A+co{s}^{2}A)=r^2$