A) \[\left\{ \frac{\pi }{3},\,\frac{2\pi }{3} \right\}\]
B) \[\left\{ \frac{\pi }{3},\,\pi \right\}\]
C) \[\left\{ \frac{2\pi }{3},\frac{4\pi }{3} \right\}\]
D) \[\left\{ \frac{2\pi }{3},\frac{5\pi }{3} \right\}\]
Correct Answer: C
Solution :
\[(5+4\cos \theta )(2\cos \theta +1)=0\] \[\cos \theta =-5/4\], which is not possible. \[\therefore 2\cos \theta +1=0\] or \[\cos \theta =-1/2\] Þ \[\theta =\frac{2\pi }{3},\,\,\frac{4\pi }{3}.\] Solution set is\[\left\{ \frac{2\pi }{3},\,\,\frac{4\pi }{3} \right\}\in [0,\,\,2\pi ]\].
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