# Mathjax is corrupted when I post an answer. [closed]

I have noticed problems when posting on Math StackExchange recently. Mathjax, whether posted by me or by others comes out garbled. Usually, all is well when I refresh the download. Most recently, while I can read others' postings just fine, my own come out as a dreadful mess, and refreshing doesn't work. I am well aware that a missing or surplus dollar sign can wreak havoc, but I have checked carefully, and I don't think that any remaining typos would cause this degree of corruption.

I have tried using a different browser, to no avail. Does anyone have an idea what might be causing this? I copy, below, my latest attempt at posting.

We may conveniently partition $$\angle BAC$$ as $$\angle BAP=18^\circ+\alpha$$ and $$\angle CAP=30^\circ-\alpha\, where$$-18^\circ<\alpha<30^\circ$$. Comparing the triangles$$BAP$$and$$CAP$$, we note that$$AP$$is common and$$|BP|=|CP|$$(since$$\triangle BPC$$is isosceles). Hence, applying the sine rule in a similar way to each triangle yields$$\sin30^\circ\sin(30^\circ-\alpha)=\sin54^\circ\sin(18^\circ+\alpha)$$, which may be written \cos60^\circ\cos(60^\circ+\alpha)=\cos36^\circ\cos(72^\circ-\alpha).\qquad\qquad(1) It is well known that$$\cos36^\circ=\frac14(\surd5+1)$$and$$\cos72^\circ=\frac14(\surd5-1)$$. (A proof is appended.) Hence$$\cos36^\circ\cos72^\circ=\frac14=\cos^260^\circ$$, and therefore$$\alpha=0$$is a solution to eqn$$1$$. Also, the LHS of eqn$$1$$is decreasing while the RHS is increasing in the given range for$$\alpha$$. Hence the solution$$\alpha=0$is unique. Appendix$$\quad$$ A property of the cosine is that $$\cos(3\times72^\circ)=-\cos36^\circ=\cos(2\times72^\circ).$$ From the identities $$\cos2\theta=2\cos^2\theta-1$$ and $$\cos3\theta=4\cos^3\theta-3\cos\theta\, it follows that$$x=\cos72^\circ$$is a solution of the cubic$$4x^3-3x=2x^2-1$$, or (x-1)(4x^2+2x-1)=0. Since$$0<\cos72^\circ<1$$, the linear factor may be ignored, and the required value is the positive root of the quadratic:$$\cos72^\circ=\frac14(\surd5-1)$$. The value$$\cos36^\circ=\frac14(\surd5+1)$ follows from the initially mentioned properties.

• Look at the spot where the rendering stops working. You have finished a math section with \$, which renders a dollar sign, rather than ending the math. Delete the \. – Xander Henderson Mod yesterday ## 1 Answer In the example you posted here on meta, you have "$$\backslash\$$" or "\\$" in several places. For example,"\$\angle CAP=30^\circ-\alpha\$" does work. But if you write "\$\angle CAP=30^\circ-\alpha\\$" then the MathJax did not end there and it does not render correctly: $$\angle CAP=30^\circ-\alpha\ The text here until the next dollar will still be considered as part of the MathJax formula$$

Let me try to copy-paste your text and remove all instances of \\\$. We may conveniently partition $$\angle BAC$$ as $$\angle BAP=18^\circ+\alpha$$ and $$\angle CAP=30^\circ-\alpha$$, where $$-18^\circ<\alpha<30^\circ$$. Comparing the triangles $$BAP$$ and $$CAP$$, we note that $$AP$$ is common and $$|BP|=|CP|$$ (since $$\triangle BPC$$ is isosceles). Hence, applying the sine rule in a similar way to each triangle yields $$\sin30^\circ\sin(30^\circ-\alpha)=\sin54^\circ\sin(18^\circ+\alpha)$$, which may be written $$\cos60^\circ\cos(60^\circ+\alpha)=\cos36^\circ\cos(72^\circ-\alpha).\qquad\qquad(1)$$ It is well known that $$\cos36^\circ=\frac14(\surd5+1)$$ and $$\cos72^\circ=\frac14(\surd5-1)$$. (A proof is appended.) Hence $$\cos36^\circ\cos72^\circ=\frac14=\cos^260^\circ$$, and therefore $$\alpha=0$$ is a solution to eqn $$1$$. Also, the LHS of eqn $$1$$ is decreasing while the RHS is increasing in the given range for $$\alpha$$. Hence the solution $$\alpha=0$$ is unique. Appendix$$\quad$$ A property of the cosine is that $$\cos(3\times72^\circ)=-\cos36^\circ=\cos(2\times72^\circ).$$ From the identities $$\cos2\theta=2\cos^2\theta-1$$ and $$\cos3\theta=4\cos^3\theta-3\cos\theta$$, it follows that $$x=\cos72^\circ$$ is a solution of the cubic $$4x^3-3x=2x^2-1$$, or $$(x-1)(4x^2+2x-1)=0.$$ Since $$0<\cos72^\circ<1$$, the linear factor may be ignored, and the required value is the positive root of the quadratic: $$\cos72^\circ=\frac14(\surd5-1)$$. The value $$\cos36^\circ=\frac14(\surd5+1)$$ follows from the initially mentioned properties. Interestingly, I am not sure how to best type backslash followed by a dollar. When I try just to enclose it by backticks, I get this: \\\$. It seems to behave in the same way when used as code (after four spaces):

$\angle CAP=30^\circ-\alpha\\\$

• Thank you very much, Martin. It seems that I fumble-fingered the backslash key instead of the shift key; but these backslashes don't show up, either in the typed code or in the output on the site. That's something I need to watch out for in future! yesterday
• I still don't understand what's going on. The copy of my post in your answer looks fine after your editing out the pesky backslashes. But when I copy and paste the code for it on the intended web page, the same old garbage appears. Help! yesterday
• @JohnBentin I have edited your answer. You can see what changes I made in the revision history. yesterday
• Thanks again, Martin. I don't know how those two rogue backslashes crept in there after I copied your perfectly rendering code. Anyway, I am very happy with the result! yesterday
• Regarding the aside at the end of your post, I had a conversation with Calvin Khor about the bug in the rendering of "backslash+dollar" beginning here: math.meta.stackexchange.com/questions/34574/… 22 hours ago