Question

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

• A. $-53/10$
• B. $-7/10$
• C. $7/10$
• D. $23/10$

Answer 1

Answer: (D)

In second quadrant $\tan ,\cot ,\cos$ are negative and sin are positive.
Given that, $3\tan A+4=0$
$\Rightarrow \tan A=-\frac{4}{3}$
Since, $A$ lies in Ilnd quadrant
$\therefore \cot A=-\frac{3}{4},\cos A=-\frac{3}{5},\sin A=\frac{4}{5}$
$\therefore 2\cot A-5\cos A+\sin A$
$=2\left(-\frac{3}{4}\right)-5\left(-\frac{3}{5}\right)+\frac{4}{5}=-\frac{3}{2}+3+\frac{4}{5}$
$=\frac{-15+30+8}{10}=\frac{23}{10}$