A) \[{{\tan }^{-1}}\,\,2\]
B) \[{{\tan }^{-1}}\,\,3\]
C) \[{{\tan }^{-1}}\,\,(-3)\]
D) \[{{\tan }^{-1}}\,\,(-2)\]
Correct Answer: C
Solution :
Given vertices of triangle are \[O(0,0),\] \[A(\cos \theta ,\,\sin \theta )\] and \[B(sin\theta ,\,-cos\,\theta )\] coordinate of centroid are \[\left( \frac{\cos \,\theta +\sin \theta }{3},\,\,\frac{\sin \theta -\cos \theta }{3} \right)\]. Since, centroid lies on the line \[y=2x.\] \[\therefore \] \[\frac{\sin \theta -\cos \theta }{3}=\frac{2\,\cos \theta +2\sin \theta }{3}\] \[\Rightarrow \] \[\sin \theta =-3\cos \theta \] \[\Rightarrow \] \[\tan \theta =-3\] \[\Rightarrow \] \[\theta ={{\tan }^{-1}}(-3)\]
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