If $x=\left(\tan ^{-1} \frac{1}{5}+\tan ^{-1} \frac{1}{8}\right)$, then $\frac{\sin x+\cos x}{\tan x}=$

If for $|x|>1, \tanh ^{-1}\left(\frac{1}{x}\right)+\operatorname{coth}^{-1}(x)=\log _e(f(x))$, then $f(-5)=$

If $\frac{1}{x^4+x^2+1}=\frac{A x+B}{x^2+x+1}+\frac{C x+D}{x^2-x+1}$, then $\cos ^{-1}(A+B+C+D)=$

The number of real roots of the equation $\sin \left[2 \cos ^{-1}\left\{\cot \left(2 \tan ^{-1} x\right)\right\}\right]=0$ that are greater than or equal to one are