I thought this one up, but I am not sure how to solve it. Here is my attempt: $$\sin x-\sqrt{3}\ \cos x=1$$ $$(\sin x-\sqrt{3}\ \cos x)^2=1$$ $$\sin^2x-2\sqrt{3}\sin x\cos x\ +3\cos^2x=1$$ $$1-2\sqrt{3}\sin x\cos x\ +2\cos^2x=1$$ $$2\cos^2x-2\sqrt{3}\sin x\cos x=0$$ $$2\cos x(\cos x-\sqrt{3}\sin ...

Hi I've been trying to figure out this algebra problem and have gotten nowhere. I'm trying to find the inverse function of this function. $f(x)=\dfrac{c^\frac{3}{2}\sqrt{c-\frac{2k}{x}}x-ck\ln\left(\frac{\left|\sqrt{c-\frac{2k}{x}}-\sqrt{c}\right|}{\sqrt{c-\frac{2k}{x}}+\sqrt{c}}\right)}{c^\frac...

Could anyone explain to me what does mathematically mean a matrix $A$ is a projector on some subspace $V\subset\mathbb R^n$ in general? Does it mean $(A^2-A)x=x\forall x\in V$? Thankx.

I suggest to remove (or even blacklist) the projection tag. The problem with this tag is that the word projection is used in many various meanings in mathematics. There is projection map in geometry and in linear algebra. In linear algebra we also have projection matrix. The term projection is ...

In connection with the discussion of projection tag I have noticed that there is the tag called map-projections. This tag was very likely created with cartography in mind. The the first occurrence found by this SEDE query is the question How do great circles project on the mercator projection?. ...