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If \( 3 \cos \theta-4 \sin \theta=2 \cos \theta+\sin \theta \), find \( \tan \theta \).
Given:
\( 3 \cos \theta-4 \sin \theta=2 \cos \theta+\sin \theta \).
To do:
We have to find \( \tan \theta \).
Solution:
We know that,
$\frac{\sin \theta}{\cos \theta}=\tan \theta$
Therefore,
$3 \cos \theta-4 \sin \theta=2 \cos \theta+\sin \theta$
$\Rightarrow 3 \cos \theta-2 \cos \theta=4 \sin \theta+\sin \theta$
$\Rightarrow \cos \theta=5 \sin \theta$
$\Rightarrow \frac{\sin \theta}{\cos \theta}=\frac{1}{5}$
$\Rightarrow \tan \theta=\frac{1}{5}$
The value of $\tan \theta$ is $\frac{1}{5}$.
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