Range of `f(x)=tan(pi[x^2-x])/[1+sin(cosx)]`,where [.] denotes greates – InterviewSolution

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1.	Range of `f(x)=tan(pi[x^2-x])/[1+sin(cosx)]`,where [.] denotes greatest integer function.
Answer» Here, we are given `x^2-x` is a greatest integer function. `:.` We can write the given expression, `f(x) = tan(npi)/(1+sin(cosx))`, here `n` is an integer. We know, `tan (npi)` is always `0`. Now, we have to check if the value of `1+sin(cosx)` is `0` or not. Let `1+sin(cosx) = 0` `=>sin(cosx) = -1` `=>cosx = -pi/2` We know, value of `cosx` lies between `-1` and `1`. So, `cosx` can not be `-pi/2`. `:. 1+sin(cosx)` can not be `0`. `:.` Value of the given expression `= tan (npi)/(1+sin(cosx)) = 0` So, option `D` is the correct option.

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