A) \[\frac{\pi }{5},\frac{\pi }{5}\]
B) \[\frac{\pi }{5}\]
C) \[\frac{\pi }{4}\]
D) None of these
Correct Answer: C
Solution :
\[\sec x\cos 5x=-1\Rightarrow \cos 5x=-\cos x\] \[\Rightarrow \] \[5x=2n\pi \pm (\pi -x)\] \[\Rightarrow \] \[x=\frac{(2n+1)\pi }{6}\text{ or }\frac{(2n-1)\pi }{4}\] Hence\[x=\frac{\pi }{4},\,\frac{\pi }{2},\,\frac{3\pi }{4},\,\frac{5\pi }{6},\,\frac{5\pi }{4},\,\frac{7\pi }{6},\,\frac{7\pi }{4},\,\frac{9\pi }{6},\,\frac{11\pi }{6}\].
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