Einstein says $$\cos\mathrm{i}x=\frac1{\sqrt{1-\left(\mathrm{i}\tan\mathrm{i}x\right)^2}},$$ but WolframAlpha says that this isn't true for $x=\pm2$ and $x=\pm9/5$. What's happening?
From page 34 of The Meaning of Relativity:
$$v=\mathrm{i}\tan\mathrm{i}\theta,\quad\mathrm{i}\sin\mathrm{i}\theta=\dfrac{v}{\sqrt{1-v^2}}\quad\text{and}\quad \cos\mathrm{i}\theta=\dfrac1{\sqrt{1-v^2}}.$$
Otherwise, the functions do appear to be identical.
Einstein is right assuming real x. $$\cos (ix) = \frac{1}{\sqrt{1-(i\tan(ix))^2}} = \frac{1}{\sqrt{1+\tan^2(ix)}} = \frac{1}{\frac{1}{\cos(ix)}}~.$$
As $\cos(ix)\gt 0$ this is an identity for all real x.