Question

If A lies in $2^{nd}$ quadrant and $3\tan A+4=0$ the prove that the value of
$2\cot A-5\cos A+\sin A$ is $\frac{23}{10}$.

Answer 1

$\tan A=-\frac{4}{3}$ and \sin ce A lies in $2^{nd}$ quadrant,
$\cos A=-ive$ and $\sin A=+ive$
$\sec A=\pm \sqrt{1-{\tan }^{2}A}=\pm \frac{5}{3}$ $\therefore$ $\cos A=-\frac{3}{5}$
$\sin A=\pm \sqrt{1-{\cos }^{2}A}=\pm \frac{4}{5}$ $\therefore$ $\sin A=\frac{4}{5}$
$\therefore$ $E=2(-\frac{3}{4})-5(-\frac{3}{5})+\frac{4}{5}$
$=-\frac{3}{2}+3+\frac{4}{5}=\frac{3}{2}+\frac{4}{5}=\frac{23}{10}$