Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If $\theta$ lies in the first quadrant and $5 \tan \theta=4$, then $\frac{5 \sin \theta-3 \cos \theta}{\sin \theta+2 \cos \theta}$ is equal to

MHT CETMHT CET 2021

Solution:

Given, $\tan \theta=\frac{4}{5}$
$\therefore \sin \theta=\frac{4}{\sqrt{41}}$ and $\cos \theta=\frac{5}{\sqrt{41}}$
Now, $\frac{5 \sin \theta-3 \cos \theta}{\sin \theta+2 \cos \theta}=\frac{5 \times \frac{4}{\sqrt{41}}-3 \times \frac{5}{\sqrt{41}}}{\frac{4}{\sqrt{41}}+2 \times \frac{5}{\sqrt{41}}}=\frac{5}{14}$