A) \[2n\pi \pm \frac{\pi }{3}\]
B) \[\pm \,2n\pi \]
C) \[\pm \,(2n+1)\frac{\pi }{2}\]
D) \[2n\pi \pm \frac{\pi }{6}\]
Correct Answer: B
Solution :
\[3\cos \theta +4\cos (\theta -x)\] \[=(3+4\cos x)\cos \theta +4\sin x.\sin \theta \] \[=\sqrt{25+24\cos x}\sin (\alpha +\theta )\] where \[\sin \theta =\frac{3+4\cos x}{\sqrt{25+24\cos x}}\] and \[\cos \theta =\frac{4\sin x}{\sqrt{25+24\cos x}}\] \[\therefore \] \[\underset{\theta \in R}{\mathop{\max }}\,(3\cos \theta +4\cos (\theta -x)\}=7\] \[\Rightarrow \]\[\sqrt{25+24\cos x}=7\] \[\Rightarrow \]\[\cos x=1\] \[\Rightarrow \]\[x=\pm \,2n\pi .\]
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