Find and simplify in expression for the idicated composite functions. State the domain using interval notation. f(x)=3x-1 g(x)=1/(x+3) Find (g@f)(x)

General form for ${\displaystyle \sin \left(kx\right)}$ in terms of ${\displaystyle \sin \left(x\right)\text{ and }\cos \left(x\right)}$
Identities for ${\displaystyle \sin \left(2x\right)}$ and ${\displaystyle \sin 3x}$, as well as their cosine counterparts are very common, and can be used to synthesize identities for ${\displaystyle \sin 4x}$ and above. Given some integer k, is there an equation to find ${\displaystyle \sin \left(kx\right)}$ in terms of ${\displaystyle \sin x}$ and ${\displaystyle \cos \left(x\right)}$?
For example, if I wanted to find the identity for ${\displaystyle \sin \left(1000x\right)}$, what would it be?
Identies used:
${\displaystyle \sin (a+b)=\sin \left(a\right)\cos \left(b\right)+\sin \left(b\right)\cos \left(a\right)}$
${\displaystyle \cos (a+b)=\cos \left(a\right)\cos \left(b\right)+\sin \left(a\right)\sin \left(b\right)}$

By polynomial formula
$(\sum _{i\in m}{x}_i{)}^n=\sum _{\begin{array}{c}{j}_i\in {\mathbb{Z}}^{+}\\ \sum j_i=n\end{array}}\left(\begin{array}{c}n\\ j_0,\dots ,j_{m-1}\end{array}\right)\prod _{i\in m}{x}_i^{j_i}$
where $n\in \mathbb{N}$
But what about $n\notin \mathbb{N}$?

For what $x^{\prime }s$ does $\sum _{k=1}^{\mathrm{\infty }}\frac{(k+1{)}^{k^2}}{k^{k^2+2}}{x}^k$ converge?

Derive the following identity:
$\tan (3x)=\frac{3\tan (x)-{\tan }^3(x)}{1-3{\tan }^2(x)}$

If ${\displaystyle \tan \left(x_1\right)\cdots \tan \left(x_n\right)=1}$ for acute ${\displaystyle x_i}$, then does it follow that ${\displaystyle \cos \left(x_1\right)+\cdots +\cos \left(x_n\right)\le n\frac{\sqrt{2}}{2}}$ ?

The absolute of the expression ${\displaystyle \frac{1+\sqrt{3}{\tan 1}^{\circ }}{\sqrt{3}-{\tan 1}^{\circ }}\cdot \frac{{\tan 89}^{\circ }}{{\cot 3}^{\circ }}}$ is equal to...

How do you find the complex conjugate of ${\displaystyle \frac{4-\sqrt{-3}}{2}}$?