A) \[0\]
B) \[1\]
C) \[2\]
D) \[3\]
Correct Answer: A
Solution :
[a] We have \[{{\cos }^{-1}}\sqrt{{{x}^{2}}+x+1}-{{\cot }^{-1}}\sqrt{x(x+1)}=\frac{\pi }{2}\] We must have \[x(x+1)\ge 0\] \[\therefore \,\,\,\,\,x(x+1)+1\ge 1\] \[\therefore \,\,\,\,\,x(x+1)+1=1\] (\[\because \,\,\,{{\cos }^{-1}}\] is defined only on \[[-1,1]\]) \[\Rightarrow \,\,\,\,\,x(x+1)=0\] \[\Rightarrow \,\,\,\,\,x\in \{0,\,-1\}\] But, none of them satisfies the equation.You need to login to perform this action.
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