Question

If $3\cos \theta -4\sin \theta =2\cos \theta +\sin \theta$, then find $\tan \theta$.

Answer 1

Given,

$3\cos \theta -4\sin \theta =2\cos \theta +\sin \theta$

Divide both sides by $\cos \theta$

$\frac{3\cos \theta -4\sin \theta }{\cos \theta }=\frac{2\cos \theta +\sin \theta }{\cos \theta }$

$\frac{3\cos \theta }{\cos \theta }-\frac{4\sin \theta }{\cos \theta }=\frac{2\cos \theta }{\cos \theta }+\frac{\sin \theta }{\cos \theta }$

$3-4\tan \theta =2+\tan \theta$

$3-2=4\tan \theta +\tan \theta$

$1=5\tan \theta$

$\tan \theta =\frac{1}{5}$