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insanepengguin135
tan(x)=7cot(x)
Can someone please help, I'm trying to review for exams!
We are solving for \(x\), I imagine.
All right: \[ \begin{align} \tan(x)&=7\cot(x)\implies\\ \tan(x)\frac{1}{\cot(x)}&=7\implies\\ \tan^2(x)&=7\implies\\ \sqrt{\tan^2(x)}&=\sqrt{7}\implies\\ |\tan(x)|&=\sqrt{7}\implies\\ x&=\tan^{-1}(\pm\sqrt 7) \end{align} \]
The general solution is: \[ x=n\pi\pm\tan^{-1}(\sqrt{7}) \]Where \(n\in \mathbb{Z}\)
Thank you! You're a lifesaver, really.