Question

If $A$ lies in the third quadrant and $3\tan A-4=0$ then find the value of $5\sin 2A+3\sin A+4\cos A$ is

• A. $0$
• B. $1$
• C. $2$
• D. none of these

Answer 1

The correct option is A $0$

$3\tan A-4=0\Rightarrow \tan A=\frac{4}{3}$
As $A$ lies in the third quadrant so
$\sin A=-\frac{4}{5}$ and $\cos A=-\frac{3}{5}$
Finding the value,
$5\sin 2A+3\sin A+4\cos A=10\sin A\cos A+3\sin A+4\cos A=10\times (-\frac{4}{5})\times (-\frac{3}{5})+3\times (-\frac{4}{5})+4\times (-\frac{3}{5})=\frac{24}{5}-\frac{12}{5}-\frac{12}{5}=0$