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Solve the following equation for B, where -A

Solve the following equation for B, where -A-example-1
User Faun
by
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1 Answer

3 votes

Given:


5\tan ^2\beta+5\tan \beta=0
5\tan \beta(\tan \beta+1)=0
\begin{gathered} 5\tan \beta=0 \\ \tan \beta=0 \\ \beta=n\pi \end{gathered}
\begin{gathered} \tan \beta+1=0 \\ \tan \beta=-1 \\ \beta=(3\pi)/(4)+n\pi \end{gathered}
\beta=n\pi,(3\pi)/(4)+n\pi\text{ , where n is any integer}

When n=0,


\beta=0,(3\pi)/(4)

When n= -1


\beta=-\pi,-(\pi)/(4)

When n= 1


\beta=\pi,(7\pi)/(4)\text{ }\Rightarrow\text{ Not valid because }-\pi\le\beta<\pi

Therefore the final answer is


\beta=-\pi,-(\pi)/(4),0,(3\pi)/(4)

User Jashwant
by
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