A) \[\left( -\frac{\pi }{2},\frac{\pi }{2} \right)-\{\,1\,\}\]
B) \[\left[ -\frac{\pi }{2},\frac{\pi }{2} \right]-\{\,1\,\}\]
C) \[\left( -\frac{\pi }{2},\frac{\pi }{2} \right)\]
D) None of these
Correct Answer: D
Solution :
We have the function \[f(x)=lo{{g}_{x}}\cos x\] \[f(x)\] is defined for\[\cos \,x>0,\] \[x>0,\] \[x\ne 1\] \[\because \] \[\cos x>0\] \[\Rightarrow \] \[-\frac{\pi }{2}<x<\frac{\pi }{2}\] Also, \[x>0,\,\,x\ne 1\] \[\therefore \] Domain of\[f\]is\[\left( 0,\,\,\frac{\pi }{2} \right)-(1)\].
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