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Prove that $\left\{ ( \sin a \cos b , \cos a\cos b , \sin b)\mid a , b \in \mathbb{N} \right\}$ is dense in the unit sphere.

Any help will be appreciated.

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    If $S_1$ is dense in $X_1$ and $S_2$ is dense in $X_2$, then $S_1 \times S_2$ is dense in $X_1 \times X_2$. If $f$ is$a$continuous map from $X$ onto $Y$ and $S$ is dense in $X$, then $f(S)$ is dense in $Y$.2012-09-04

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Because $\cos(n)$ and $\sin(n)$ (for n an integer) are dense on the interval $[0,1]$ (because $\pi$ is irrational) and those map continu to your coordinates.

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    I suspect the re$a$son you got downvotes is that that you $b$asically just copied Robert Israel's comme$n$t from above (without eve$n$ saying so).2012-09-04