Question

If $\sin A:\cos A=4:7$, then the value of $\frac{7\sin A-3\cos A}{7\sin A+2\cos A}$ is

• A. $\frac{3}{14}$
• B. $\frac{3}{2}$
• C. $\frac{1}{3}$
• D. $\frac{1}{6}$

Answer 1

The correct option is D $\frac{1}{6}$

$\frac{\sin A}{\cos A}=\frac{4}{7}$

$S=\frac{7\sin A-3\cos A}{7\sin A+2\cos A}$

Divide numerator and denominator by $\cos A$, we get

$S=\frac{7\frac{\sin A}{\cos A}-3}{7\frac{\sin A}{\cos A}+2}=\frac{4-3}{4+2}=\frac{1}{6}$

Hence, option D.