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Sign of Trigonometric Ratios in Different Quadrants

Range of f x ...

Question

Range of $f (x) = \frac{t a n (π [x^{2} - x])}{1 + s i n (c o s x)}$ is (where [x] denotes the greatest integer function

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[tan 2, tan 1]

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{0}

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Solution

The correct option is D {0}
$f (x) = \frac{t a n (π [x^{2} - x])}{1 + s i n x (c o s x)} = {0}$ because of $[x^{2} - x]$ is integer

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