Question

If $\frac{\cos A}{3}=\frac{\cos B}{4}=\frac{1}{5},\frac{-\pi }{2}<A,B<0$ then $2\sin A+4\sin B=....$

• A. $4$
• B. $2$
• C. $-4$
• D. $0$

Answer 1

Answer: (A)

$4$

If $\frac{\cos A}{3}=\frac{\cos B}{4}=\frac{1}{5}\cos A=\frac{3}{5},\cos B=\frac{4}{5}\therefore \sin A=\frac{\sqrt{5^2-3^2}}{5},\sin B=\frac{\sqrt{5^2-4^2}}{5}\sin A=\frac{4}{5},\sin B=\frac{3}{5}Then2\sin A+4\sin B=2\times \frac{4}{5}+4\times \frac{3}{5}=\frac{8}{5}+\frac{12}{5}=\frac{20}{5}=4$