Find the general solution of : 3 =-1 - Vidyadip

Question

Find the general solution of : $\tan 3 \theta=-1$

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Answer

(ii) We have $\tan 3 \theta=-1$
$
\therefore \quad \tan 3 \theta=\tan \frac{3 \pi}{4}\left(A s \tan \frac{\pi}{4}=1 \text { and } \tan (\pi-A)=-\tan A\right)
$
The general solution of $\tan \theta=\tan \alpha$ is $\theta= n \pi+\alpha$, where $n \in Z$.
$\therefore \quad$ The general solution of $\tan 3 \theta=\tan \frac{3 \pi}{4}$ is $3 \theta= n \pi+\frac{3 \pi}{4}$ where $n \in Z$.
$\therefore \quad$ The general solution of $\tan 3 \theta=-1$ is $\theta=\frac{n \pi}{3}+\frac{\pi}{4}$, where $n \in Z$.

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