What is wrong with my proof?(adsbygoogle = window.adsbygoogle || []).push({});

Let [tex]\theta=cos^{-1}x-\frac{\pi}{2}[/tex]

Then [tex]cos\theta=cos\left(cos^{-1}x-\frac{\pi}{2}\right)[/tex]

[tex]RHS=xcos\frac{\pi}{2}-sin(cos^{-1}x)sin\frac{\pi}{2}[/tex]

[tex]=-\sqrt{1-x^2}[/tex]

Therefore [tex]\theta=cos^{-1}(-\sqrt{1-x^2})[/tex]

[tex]\theta=\pi-cos^{-1}\sqrt{1-x^2}[/tex]

Hence [tex]cos^{-1}x-\frac{\pi}{2}=\pi-cos^{-1}\sqrt{1-x^2}[/tex]

So finally, [tex]cos^{-1}x+cos^{-1}\sqrt{1-x^2}=\frac{3\pi}{2}[/tex]

Except this is untrue for all values except [itex]x=-1[/itex]. I'm guessing I probably made a substitution which is valid for only certain values. Inverse trig seems to do that a lot to me

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Proof incorrect

**Physics Forums | Science Articles, Homework Help, Discussion**