cdsommegolfzp

2022-07-06

Is $\mathrm{cot}\left(x\right)=\frac{1}{\mathrm{tan}\left(x\right)}$?

Jaruckigh

Expert

we have $\mathrm{cot}\left(x\right)=\frac{\mathrm{cos}\left(x\right)}{\mathrm{sin}\left(x\right)}$ and $x\ne k\pi$ $k\in \mathbb{Z}$ and $\mathrm{tan}\left(x\right)=\frac{\mathrm{sin}\left(x\right)}{\mathrm{cos}\left(x\right)}$ and $x\ne \frac{2k+1\right)}{2}\pi$ and$\frac{1}{\mathrm{tan}\left(x\right)}$
is defined for all x with $\mathrm{tan}\left(x\right)\ne 0$ and this is if $\mathrm{sin}\left(x\right)\ne 0$ if $x\ne k\pi$ with $x\in \mathbb{Z}$

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