Question

If $5\tan \theta =4$, then find the value of $\frac{5\sin \theta -3\cos \theta }{5\sin \theta +2\cos \theta }$.

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

Answer 1

Answer: (A)

$\frac{1}{6}$

$5\tan \theta =4$ i.e. $\tan \theta =\frac{4}{5}$
$\frac{5\sin \theta -3\cos \theta }{5\tan \theta +2\cos \theta }$,
Dividing numerator and denominator by $\cos \theta =\frac{5\tan \theta -3}{5\tan \theta +2}$
$=\frac{5\times \frac{4}{5}-3}{5\times \frac{4}{5}+2}=\frac{4-3}{4+2}=\frac{1}{6}$