Question

Solve this :

$11.\mathrm{If}3\cot \mathrm{\theta }=2,\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}\frac{4\sin \mathrm{\theta }-3\cos \mathrm{\theta }}{2\sin \mathrm{\theta }+6\cos \mathrm{\theta }}$

Answer 1

$$\begin{gathered} 11. \\ cot\theta =\frac{2}{3}=\frac{B}{P} \\ B=2,P=3,H=\sqrt{4+9}=\sqrt{13} \\ \sin \theta =\frac{3}{\sqrt{13}},\cos \theta =\frac{2}{\sqrt{13}} \\ \frac{4\sin \theta -3\cos \theta }{2\sin \theta +6\cos \theta }=\frac{\frac{12}{\sqrt{13}}-\frac{6}{\sqrt{13}}}{\frac{6}{\sqrt{13}}+\frac{12}{\sqrt{13}}}=\frac{6}{18}=\frac{1}{3} \\ Regards \end{gathered}$$