If $\;x = r\,\,\sin \,\,{\rm{\theta }}\,\,\cos \,\,\phi ,\;\,y = r\,\,\sin \,\,{\rm{\theta }}\,\,\sin \,\,\phi {\rm{\;and\;z}} = r\,\,\cos \,\,{\rm{\theta }}$, then the value of ${x^2} + {y^2} + {{\rm{z}}^2}$ is independent of

JEE MATHEMATICS MCQ: TRIGONOMETRY RATIOS

1 Easy

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Understanding +4 | -1

\;x = r\,\,\sin \,\,\mathrm{\theta }\,\,\cos \,\,\phi ,\;\,y = r\,\,\sin \,\,\mathrm{\theta }\,\,\sin \,\,\phi \mathrm{\;and\;z} = r\,\,\cos \,\,\mathrm{\theta }

, then the value of

{x^2} + {y^2} + {\mathrm{z}^2}

is independent of

View answer and explanation

Correct option: A

\mathrm{\theta },\,\,\phi

Option A (

\mathrm{\theta },\,\,\phi

) is correct because

{x^2} + {y^2} + {\mathrm{z}^2}

simplifies to

{r^2}

, which is independent of

\mathrm{\theta }

and

\phi