Question

If $5\tan \theta =4,$ then find the value of $\frac{(5\sin \theta -4\cos \theta )}{(5\sin \theta +4\cos \theta )}$.

Answer 1

On dividing both the numerator and denominator by $\cos \theta$ we get,

$\frac{(5\sin \theta -4\cos \theta )}{(5\sin \theta +4\cos \theta )}$

$=\frac{\frac{(5\sin \theta -4\cos \theta )}{\cos \theta }}{\frac{(5\sin \theta +4\cos \theta )}{\cos \theta }}$

$=\frac{5\tan \theta -4}{5\tan \theta +4}$

$=\frac{4-4}{4+4}=0$ [ Given: $5\tan \theta =4$ ]

$\therefore \frac{(5\sin \theta -4\cos \theta )}{(5\sin \theta +4\cos \theta )}=0$