| Statement-1: The domain of the function\[f(x)=\sqrt{{{\log }_{2}}\sin x}\]is\[(4n+1)\frac{\pi }{2},\,\,n\in N\]. |
| Statement-1: Expression under even root should be\[\ge 0\]. |
A) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
B) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
C) Statement-1 is true, Statement-2 is false.
D) Statement-1 is false, Statement-2 is true.
Correct Answer: A
Solution :
For\[f(x)\]to be real\[{{\log }_{2}}(\sin x)\ge 0\] \[\Rightarrow \]\[\sin x\ge {{2}^{o}}\Rightarrow \sin x=1\] \[\Rightarrow \]\[x=(4n+1)\frac{\pi }{2},\,\,n\in N\].
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