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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Updated on: 10-Oct-2022

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