Question

If $5\cot \theta =4$ then the value of $\left(\frac{5\sin \theta -3\cos \theta }{\sin \theta +2\cos \theta }\right)$ is :

• A. $\frac{5}{14}$
• B. $\frac{3}{4}$
• C. 1
• D. None of these

Answer 1

Answer: (C)

1

$\left(\frac{5\sin \theta -3\cos \theta }{\sin \theta +2\cos \theta }\right)$
Dividing numerator and denominator by $\sin \theta$ we get:
$=\frac{5-3\cot \theta }{1+2\cot \theta }=\frac{5-3\times \frac{4}{5}}{1+2\times \frac{4}{5}}=1$