A) \[0\]
B) \[\frac{-\,\,24}{5}\]
C) \[\frac{24}{5}\]
D) \[\frac{48}{5}\]
Correct Answer: A
Solution :
| \[3\tan \theta =4\]\[\Rightarrow \]\[\sin \theta =\frac{-\,\,4}{5}\]and \[\cos \theta =\frac{-\,\,3}{5}\] |
| \[\therefore \] \[5\sin 2\theta +3\sin \theta +4\cos \theta \] |
| \[=10\sin \theta \cos \theta +3\sin \theta +4\cos \theta \] |
| \[=10\left( \frac{-\,\,4}{5} \right)\left( \frac{-\,\,3}{5} \right)+3\left( \frac{-\,\,4}{5} \right)+4\left( \frac{-\,\,3}{5} \right)\] |
| \[=10\left( \frac{12}{25} \right)-\frac{12}{5}-\frac{12}{5}=\frac{24}{5}-\frac{24}{5}=0\] |
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