A) \[{{r}^{2}}\,{{\cos }^{2}}\phi \]
B) \[{{r}^{2}}\,{{\sin }^{2}}\theta +{{r}^{2}}{{\cos }^{2}}\phi \]
C) \[{{r}^{2}}\]
D) \[\frac{1}{{{r}^{2}}}\]
Correct Answer: C
Solution :
\[{{x}^{2\text{ }}}+\text{ }{{y}^{2}}+\text{ }{{z}^{2}}\] \[={{r}^{2}}si{{n}^{2}}\theta co{{s}^{2}}\phi +{{r}^{2}}si{{n}^{2}}\theta si{{n}^{2}}\phi +{{r}^{2}}co{{s}^{2}}\theta \] \[={{r}^{2}}si{{n}^{2}}\theta (co{{s}^{2}}\phi +{{r}^{2}}si{{n}^{2}}\phi )+{{r}^{2}}co{{s}^{2}}\theta \] \[={{r}^{2}}si{{n}^{2}}\theta +{{r}^{2}}co{{s}^{2}}\theta \] \[={{r}^{2}}(si{{n}^{2}}\theta +co{{s}^{2}}\theta )={{r}^{2}}\]
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