Question

If $A$ lies in the second quadrant and $3\tan A+4=0$, then 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 $\frac{23}{10}$

$tanA=-4/3$
Then the value of other trigonometric ratios present in the expression would be
$cotA=-\frac{3}{4}$
$sinA=\frac{4}{5}$
$cosA=-\frac{3}{5}$
Hence the value of the expression $2cotA-5cosA+sinA=-\frac{3}{2}+3+\frac{4}{5}=\frac{23}{10}$
Hence, option B is the correct option