Question

Solve. Find all solutions in [0,2).5 secx cotx+5 secx+ cotx+1=0

Answer 1

`\begin{gathered} 5sec(x)cot(x)+5sec(x)+cot(x)+1=0 \\ Factoring \\ (cot(x)+1)(5sec(x)+1)=0 \\ cot(x)+1=0 \\ cot(x)=-1 \\ x=cot^(-1)(1) \\ x=(3\pi)/(4) \\ \\ 5sec(x)+1=0 \\ 5sec(x)=-1 \\ sec(x)=(-1)/(5),\text{ there is no solution} \\ Hence \\ All\text{ solution are }(3\pi)/(4)+\pi n,\text{ where n=1,2,3...} \\ \\ \end{gathered}`