<s>[INST] Inverse trigonometric equation and finding value of given expression If $\arctan(4) = 4 \arctan(x)$ then value of $x^5-7x^3+5x^2+2x+9870$ is?
I used $2\arctan(x) = \arctan(2x/1-x^2)$ twice for RHS of the equation which gave me $x^4+x^3-6x^2-x+1=0$ and I am clueless how to proceed after that.
Also I am not sure about using the formula I mentioned as its valid only when $|x|<1$.
Please help me in this regard
 [/INST] Hint
From where you have left, use
$$x^5-7x^3+5x^2+2x=x(x^4+x^3-6x^2-x+1)-(x^4+x^3-6x^2-x+1)+1$$
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