Question

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

• A. $\frac{52}{10}$
• B. $\frac{23}{10}$
• C. $\frac{37}{10}$
• D. $\frac{7}{10}$

Answer 1

The correct option is B

$\frac{23}{10}$

Given equation, 3 tan A +4 =0

$\Rightarrow 3tanA=-4\Rightarrow tanA=\frac{-4}{3}$

$\Rightarrow cotA=\frac{-3}{4}$

$\Rightarrow secA=\sqrt{1+\frac{16}{9}}=\sqrt{\frac{25}{9}}=\pm \frac{5}{3}$

$\Rightarrow secA=\frac{-5}{3}$

[since, A lies in second quadrant]

$cosA=\frac{-3}{5}$

$sinA=\sqrt{1-\frac{9}{25}}=\frac{\sqrt{25-9}}{25}=\pm \frac{4}{5}$

$sinA=\frac{4}{5}$

[since, A lies in second quadrant]

$\therefore 2cotA-5cosA+sinA$

$=2\left(\frac{-3}{4}\right)-5\left(\frac{-3}{5}\right)+\frac{4}{5}=\frac{-6}{4}+3+\frac{4}{5}.$

$=\frac{-30+60+16}{20}=\frac{46}{20}=\frac{23}{10}$