If $\cos ^3 80^{\circ}+\cos ^3 40^{\circ}-\cos ^3 20^{\circ}=k$, then $\frac{4 k}{3}=$
$\sin \left(\frac{4 \pi}{3}\right)$
$\cos \left(\frac{2 \pi}{3}\right)$
$\tan \left(\frac{\pi}{3}\right)$
$\sec \left(\frac{2 \pi}{3}\right)$
The number of solutions of the equation $4 \cos 2 \theta \cos 3 \theta=\sec \theta$ in the interval $[0,2 \pi]$ is
12
8
16
4
$$ \tan \left(2 \tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{7}\right)\right)= $$
$\frac{1}{\sqrt{3}}$
$\sqrt{3}$
1
$3 / 7$
$$ \tanh ^{-1}\left(\frac{1}{3}\right)+\operatorname{coth}^{-1}(3)= $$
$\operatorname{sech}^{-1}\left(\frac{1}{3}\right)$
$\operatorname{cosech}^{-1}\left(\frac{1}{3}\right)$
$\cosh ^{-1}\left(\frac{4}{3}\right)$
$\sinh ^{-1}\left(\frac{3}{4}\right)$
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