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ivann1987 [24]
11 months ago
12

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

Mathematics
1 answer:
Dmitrij [34]11 months ago
5 0
\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=\frac{3\pi}{4} \\  \\ 5sec(x)+1=0 \\ 5sec(x)=-1 \\ sec(x)=\frac{-1}{5},\text{ there is no solution} \\ Hence \\ All\text{ solution are }\frac{3\pi}{4}+\pi n,\text{ where n=1,2,3...} \\  \\  \end{gathered}

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