Question

tan(x)=7cot(x)

Answer 1

Can someone please help, I'm trying to review for exams!

Answer 2

We are solving for \(x\), I imagine.

Answer 3

Oh, yes.

Answer 4

All right:
\[
\begin{align}
\tan(x)&=7\cot(x)\implies\\
\tan(x)\frac{1}{\cot(x)}&=7\implies\\
\tan^2(x)&=7\implies\\
\sqrt{\tan^2(x)}&=\sqrt{7}\implies\\
|\tan(x)|&=\sqrt{7}\implies\\
x&=\tan^{-1}(\pm\sqrt 7)
\end{align}
\]

Answer 5

The general solution is:
\[
x=n\pi\pm\tan^{-1}(\sqrt{7})
\]Where \(n\in \mathbb{Z}\)

Answer 6

Thank you! You're a lifesaver, really.

Answer 7

Sure thing