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Range of f(x)=tan(pi[x^2-x])/[1+sin(cosx...

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

Text Solution

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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`
...
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