A) \[\pm \frac{\pi }{3},\pm \frac{2\pi }{3}\]
B) \[\frac{\pi }{3},\frac{2\pi }{4}\]
C) \[\frac{\pi }{4},\frac{3\pi }{4}\]
D) None of these
Correct Answer: A
Solution :
[a] Since, \[0<x<\pi ,-1<\cos x<1\Rightarrow 0\le |\cos x|<1\]. We can write the given expression as \[{{11}^{1/(1-|\cos x|)}}=121\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\frac{1}{1-\left| \cos x \right|}=2\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,1-\left| \cos x \right|=\frac{1}{2}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\left| \cos x \right|=\frac{1}{2}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\cos x=\pm \frac{1}{2}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,x=\pm \frac{\pi }{3},\,\,\pm \frac{2\pi }{3}\]
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