question_answer

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) \[23/10\]

Correct Answer: D

Solution :

Key Idea: 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 IInd quadrant \[\therefore \]  \[\cot A=-\frac{3}{4},\,\,\cos A=-\frac{3}{5},\,\,\sin A=\frac{4}{5}\] \[\therefore \]  \[2\cot A-5\cos A+\sin A\]                 \[=2\left( -\frac{3}{4} \right)-5\left( -\frac{3}{5} \right)+\frac{4}{5}\]                 \[=-\frac{3}{2}+3+\frac{4}{5}\]                 \[=\frac{-15+30+8}{10}=\frac{23}{10}\]