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

Question

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.

Answer 1

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\\\$