A) \[\frac{\pi }{5},\,\,\frac{\pi }{4}\]
B) \[\frac{\pi }{5}\]
C) \[\frac{\pi }{4}\]
D) None of these
Correct Answer: C
Solution :
We have,\[\sec x\cos 5x+1=0\] \[\Rightarrow \] \[\sec x\cos 5x=-1\] \[\Rightarrow \] \[\cos 5x=-\cos x\] \[\Rightarrow \] \[5x=2n\pi \pm (\pi -x)\] \[\Rightarrow \] \[x=\frac{(2n+1)\pi }{6}or\frac{(2n-1)\pi }{4}\] 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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