Question

If A lies in the second quadrant and $3\tan A+4=0$, the value of $2\cot A-5\cos A+\sin A$ is equal to

• A. $-\frac{53}{10}$
• B. $\frac{23}{10}$
• C. $-\frac{37}{10}$
• D. $\frac{7}{10}$

Answer 1

The correct option is B $\frac{23}{10}$

$3\tan A+4=0\Rightarrow \tan A=-\frac{4}{3}=\frac{p}{b}\Rightarrow p=4x,b=3x\Rightarrow h=\sqrt{p^2+b^2}=\pm 5x$
As A is in II quadrant
$\sin A=\frac{4}{5}$ and $\cos A=-\frac{3}{5}$
Therefor
$2cotA-5\cos A+\sin A=-2.\frac{3}{4}-5(-\frac{3}{5})+\frac{4}{5}=\frac{23}{10}$