A) \[2\]
B) \[4\]
C) \[6\]
D) \[8\]
Correct Answer: C
Solution :
[c] \[{{\cot }^{2}}(\sin x+3)=1={{\cot }^{2}}\frac{\pi }{4}\] \[\Rightarrow \,\,\,\sin \,x+3=n\pi \pm \frac{\pi }{4}\] Now, \[2\le \sin x+3\le 4\] \[\therefore \,\,\,\sin x+3=\pi -\frac{\pi }{4}\] or \[\sin x+3=\pi +\frac{\pi }{4}\] \[\Rightarrow \,\,\,\sin x=\frac{3\pi }{4}-3\] or \[\sin x=\frac{5\pi }{4}-3\] Hence, there are six solutions.You need to login to perform this action.
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