A) \[\frac{24}{25}\]
B) \[-\frac{24}{25}\]
C) \[\frac{13}{18}\]
D) \[-\frac{13}{18}\]
Correct Answer: A
Solution :
Since, \[\alpha \] is a root of \[25{{\cos }^{2}}\theta +5\cos \theta -12=0\] \[\therefore \] \[25{{\cos }^{2}}\alpha +5\cos \alpha -12=0\] \[\Rightarrow 25{{\cos }^{2}}\alpha +20\cos \alpha -15\cos \alpha -12=0\] \[\Rightarrow \] \[5(5\cos \alpha +4)\,\,(5\cos \alpha -3)=0\] \[\Rightarrow \] \[(5\cos \alpha +4)\,(5\cos \alpha -3)=0\] \[\Rightarrow \] \[\cos \alpha =-\frac{4}{5},\frac{3}{5}\] But \[\frac{\pi }{2}<\alpha <\pi \] in second quadrant. \[\therefore \] We take \[\cos \alpha =-\frac{4}{5}\] \[(\because \cos \alpha <0)\] \[\Rightarrow \] \[\sin \alpha =\frac{3}{5}\] \[\therefore \sin 2\alpha =2\sin \alpha \cos \alpha =-2\times \frac{3}{5}\times \frac{4}{5}=-\frac{24}{25}\]
You need to login to perform this action.
You will be redirected in
3 sec
