${lim}_{x \to \frac{π}{2}} \frac{s i n x}{c o s^{- 1} [\frac{1}{4} (3 s i n x - s i n 3 x)]}$ equals to (where [.] denotes greatest integer function)

\frac{2}{π}

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\frac{4}{π}

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Does not exist

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Solution

The correct option is A $\frac{2}{π}$
${lim}_{x \to \frac{π}{2}} \frac{s i n x}{c o s^{- 1} [s i n^{3} x]} \Rightarrow \frac{s i n \frac{π}{2}}{c o s^{- 1} (0)} = \frac{1}{\frac{π}{2}} = \frac{2}{π}$

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