I have a question regarding the answer of @Sandy G of the following one: Procedure for obtaining the formulas of the half angle

I'm trying to do the same but for other formula:



    -\cos^2 \left( \dfrac{\alpha}{2}\right) &+\sin^2 \left( \dfrac{\alpha}{2}\right) &&=-\cos \alpha \\
    \cos^2 \left( \dfrac{\alpha}{2}\right) &+\sin^2 \left( \dfrac{\alpha}{2}\right) &&=1\\[-1ex]
    &\rlap{\rule{5.1cm}{.5pt}} \\[-1ex]
    2&\sin^2 \left( \dfrac{\alpha}{2}\right)&&= 1-\cos \alpha \Rightarrow \sin^2 \left( \dfrac{\alpha}{2}\right)=\dfrac{1-\cos \alpha}{2}\Rightarrow \sin \left( \dfrac{\alpha}{2}\right) = \pm \sqrt{\dfrac{1-\cos \alpha}{2}}

The result is: enter image description here

But the line is offset to the left and the $2\sin^2$ if it could be glued to the equal symbol....

  • 2
    Look closer to your & placements. And please edit your question to give a full MWE.
    – SebGlav
    Feb 20, 2023 at 9:19
  • 1
    @SebGlav, I tried to play with the positions of the &, but I didn't succeed. Feb 20, 2023 at 10:29

1 Answer 1


You could pad it with some hspace for a quick and dirty fix:

    -&\cos^2 \left( \dfrac{\alpha}{2}\right) + \sin^2 \left( \dfrac{\alpha}{2}\right)&&=-\cos \alpha \\
    &\cos^2 \left( \dfrac{\alpha}{2}\right) +\sin^2 \left( \dfrac{\alpha}{2}\right)&&=1\\[-1ex]
    &\hspace{4.7em}2\sin^2 \left( \dfrac{\alpha}{2}\right)&&= 1-\cos \alpha \Rightarrow \sin^2 \left( \dfrac{\alpha}{2}\right)=\dfrac{1-\cos \alpha}{2}\Rightarrow \sin \left( \dfrac{\alpha}{2}\right) = \pm \sqrt{\dfrac{1-\cos \alpha}{2}}


sin half angle derivation

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