Question

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

• A. $\frac{5}{3}$
• B. $\frac{5}{6}$
• C. $\frac{1}{6}$
• D. 0

Answer 1

The correct option is D

0

If we express the given equation in the form of $\tan \theta$, then it will be easier to solve.

Hence, 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: $5\tan \theta =4$ ]

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