A) 1
B) 3
C) 2
D) zero
Correct Answer: C
Solution :
\[|\cot x|=\cot x+\frac{1}{\sin x}\] Let \[\cot x>0\Rightarrow \cot x=\cot x+\frac{1}{\sin x}=0\] \[\Rightarrow \]\[\frac{1}{\sin x}=0,\] Let\[\cot x\le 0\] \[\Rightarrow \]\[-\cot x=\cot x+\frac{1}{\sin x}\]\[\Rightarrow \]\[-2\cot x=\frac{1}{\sin x}\] \[\Rightarrow \]\[\cos x=-\frac{1}{2}\Rightarrow x=\frac{2\pi }{3},\frac{8\pi }{3}\] \[\therefore \]The number of solutions are 2.
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