1. Tardigrade
  2. Question
  3. Mathematics
  4. If 5 tan θ=4, then (5 sin θ-3 cos θ/5 sin θ+2 cos θ)=

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

Trigonometric Functions

Solution:

$5 \,\tan \,\theta=4 \Rightarrow \tan\,\theta=\frac{4}{5}$
$\therefore \sin \,\theta=\frac{4}{\sqrt{41}}$ and $\cos\, \theta=\frac{5}{\sqrt{41}}$
$\frac{5 \,\sin \,\theta-3 \cos \,\theta}{5 \,\sin 0+2\, \cos 0}=\frac{5 \times \frac{4}{\sqrt{41}}-3 \times \frac{5}{\sqrt{41}}}{5 \times \frac{4}{\sqrt{41}}+2 \times \frac{5}{\sqrt{41}}}=\frac{1}{6} .$