Fundamental trigonometric equation

We want to solve some fundamental equations:

$$\sin x=a,\: -1\leq a\leq 1$$
$$\cos x=a,\: -1\leq a\leq 1$$
$$\tan x=a,\: -\infty <a<+\infty$$
$$\cot x=a,\: -\infty <a<+\infty$$

Each of these equations has a countable set of solutions.

$$\sin x=a,\: -1\leq a\leq 1;\: x_k=k\pi+(-1)^k \arcsin a$$

$$\cos x=a,\: -1\leq a\leq 1;\: x_k=2k\pi\pm  \arccos a$$

$$\tan x=a,\: -\infty <a<+\infty;\: x_k=k\pi+ \arctan a$$

$$\cot x=a,\: -\infty <a<+\infty:\: x_k=k\pi+ \cot^{-1} a$$

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