Trigonometric Identities Question 141
Question: If $ A $ lies in the second quadrant and $ 3\tan A+4=0, $ the value of $ 2\cot A-5\cos A+\sin A $ is equal to
[Pb. CET 2000]
Options:
A) $ \frac{-53}{10} $
B) $ \frac{-7}{10} $
C) $ \frac{7}{10} $
D) $ \frac{23}{10} $
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Answer:
Correct Answer: D
Solution:
$ 3,\tan A+4=0,\Rightarrow ,\tan A=-\frac{4}{3} $
$ \Rightarrow \sin A,=\pm ,\frac{\tan A}{\sqrt{1+{{\tan }^{2}}A}}=\pm \frac{-4/3}{\sqrt{1+16/9}}=-\frac{4}{5} $ $ (\because A $ is in 2nd quadrant) and $ \cos ,A=-\frac{3}{5} $ . Thus, $ 2\cot A-5\cos A+\sin A $ $ =2,( -\frac{4}{3} )-5,( -\frac{3}{5} )+\left( -\frac{4}{5} \right)=\frac{23}{10} $ .
BETA
