Prove that: \(\displaystyle{\tan{{\left({2}{{\tan}^{{-{1}}}{\left({x}\right)}}\right)}}}={2}{\tan{{\left({{\tan}^{{-{1}}}{\left({x}\right)}}+{{\tan}^{{-{1}}}{\left({x}^{{3}}\right)}}\right)}}}\) My Attempt \(\displaystyle{{\tan}^{{-{1}}}{\left({x}\right)}}={A}\) \(\displaystyle{x}={\tan{{\left({A}\right)}}}\) Now,

Describe all solutions of Ax=0 in parametric vector form, where A is row equivalent to the given matrix
$$\left[\begin{array}{cccc}1& 3& 0& -4\\ 2& 6& 0& -8\end{array}\right]$$

Find, correct to the nearest degree, the three angles of the triangle with the given vertices
A(1, 0, -1), B(3, -2, 0), C(1, 3, 3)

Whether f is a function from Z to R if 
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b) ${\displaystyle f\left(n\right)=\sqrt{n^2+1}}$. 
c) ${\displaystyle f\left(n\right)=\frac{1}{n^2-4}}$.

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Find $\tan \left(22.5^{\circ }\right)$ using the half-angle formula.

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The solution set of $\tan <!--\; \; -->\mathrm{\theta <!--\; \theta \; -->}=3\cot <!--\; \; -->\mathrm{\theta <!--\; \theta \; -->}$ is

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