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If tan(x) + sec(x) = 22/7, what is tan(x)?

Hello Guest!

\(tan(x) + sec(x) = \frac{22}{7}\)

\(tan(x)\ \pm \sqrt{1+tan^2(x)}= \frac{22}{7}\)          \(tan(x)\ is\ u.\ \frac{22}{7}\ is\ \pi.\)  

\(u\pm\sqrt{1+u^2}=\pi\\ \pm\sqrt{1+u^2}=\pi-u\\ 1+u^2=\pi^2-2u\cdot \pi+u^2\\ \pi^2-2\pi u-1=0\)

\(2\pi u=\pi^2-1\\ u=\frac{\pi^2-1}{2\pi}= \frac{\pi}{2}-\frac{1}{2\pi}\)                           \(\pi \ is\ \frac{22}{7}\)

\(u=\frac{22}{14}-\frac{7}{2\cdot 22}= \frac{11}{7}-\frac{7}{44}=\frac{44\cdot 11-49}{7\cdot 44}=\frac{435}{308}=\color{blue}1.41233766234\)

\(tan(x)=1.41233766\)

  !