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Express tan(nx) as a rational function of tan(x) for n = 1,2,3,4,5,6.

> expand(tan(x));

tan(x)

> expand(tan(2*x));

2*tan(x)/(1-tan(x)^2)

> expand(tan(3*x));

(3*tan(x)-tan(x)^3)/(1-3*tan(x)^2)

> expand(tan(4*x));

(4*tan(x)-4*tan(x)^3)/(1-6*tan(x)^2+tan(x)^4)

> expand(tan(5*x));

(5*tan(x)-10*tan(x)^3+tan(x)^5)/(1-10*tan(x)^2+5*ta...

> expand(tan(6*x));

(6*tan(x)-20*tan(x)^3+6*tan(x)^5)/(1-15*tan(x)^2+15...

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