1.

The range of the following function is`f(x)=sqrt((1-cosx)sqrt((1-cosx)sqrt((1-cosx)sqrt(oo))))`(0,1) (b) `(0,1/2)`(c) `(0,2)`(d) `non eoft h e s e`A. [0, 1]B. [0, 1/2]C. [0, 2)D. None of these

Answer» Correct Answer - C
Given `f(x)=sqrt((1-cosx)sqrt((1-cosx)sqrt((1-cosx)sqrt(...oo))))`
` =(1-cosx)^((1)/(2))(1-cosx)^((1)/(4))(1-cosx)^((1)/(8)) ...oo`
`=(1-cosx)^((1)/(2)+(1)/(4)+(1)/(8)+ ...oo)`
`=(1-cosx)^((1//2)/(1-(1//2)))`
`=1-cosx`
Thus, the range of `f(x)` is `[0,2).`


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