Question

If $5\tan \theta =4$ then $\frac{5\sin \theta -3\cos \theta }{5\sin \theta +2\cos \theta }$ is equal to

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

Answer 1

Answer: (C)

$\frac{1}{6}$

$\frac{5sin\theta -3cos\theta }{5sin\theta +2cos\theta }=\frac{5tan\theta -3}{5tan\theta +2}$ [dividing num and denominator by $\cos \theta$]
Substituting $tan\theta =\frac{4}{5}$, we get
$\frac{5\frac{4}{5}-3}{5\frac{4}{5}+2}=\frac{1}{6}$