$l i m x \to 0 \frac{t a n ([- π^{2}] x^{2}) - t a n (- π^{2}) x^{2}}{s i n^{2} x}$ equals (where [.] denotes the greatest integer function)

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tan 10 - 10

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Solution

The correct option is B tan 10 - 10
$∵ π = 3.14 ∴ π^{2} = 9.86 ∴ [- π^{2}] = [- 9.86] = - 10 T h e n l i m x \to 0 \frac{t a n ([- π^{2}] x^{2}) - t a n ([- π^{2}] x^{2})}{s i n^{2} x} = l i m x \to 0 \frac{t a n ([- π^{2}] x^{2}) - t a n ([- π^{2}] x^{2})}{s i n^{2} x} = l i m x \to 0 \frac{\frac{t a n (- 10 x^{2})}{(- 10 x^{2})} . (- 10) + t a n 10. \frac{x^{2}}{x^{2}}}{s i n^{2} x} = \frac{(1) (- 10) + t a n 10.1}{(1)^{2}} = t a n 10 - t a n 10$

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