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I have the the following expression:

$ tan(m \cdot actan(x) + n \cdot arctan(y))$

For what values of $n,m \in \mathbb{N}$ is this expression reducible to a rational expression in $R[x,y], where R is generic ring$?

Is there some rule $lhs => rhs $ that is needed in order to get a rational expression form the expression above?

I have the the following expression:

$ tan(m \cdot actan(x) + n \cdot arctan(y))$

For what values of $n,m \in \mathbb{N}$ is this expression reducible to a rational expression in $R[x,y], $R[x,y]$, where R $R$ is generic ring$?

Is there some rule $lhs => rhs $ that is needed in order to get a rational expression form the expression above? above?

I have the the following expression:

$ tan(m \cdot actan(x) + n \cdot arctan(y))$

For what values of $n,m \in \mathbb{N}$ is this expression reducible to a rational expression in $R[x,y]$, where $R$ is generic ring$? ring?

Is there some rule $lhs => rhs $ that is needed in order to get a rational expression form the expression above?

I have the the following expression:

$ tan(m \cdot actan(x) + n \cdot arctan(y))$

For what values of $n,m \in \mathbb{N}$ is this expression reducible to a rational expression in $R[x,y]$, where $R$ is a generic ring?

Is there some rule $lhs => rhs $ that is needed in order to get a rational expression form the expression above?