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Relation between Inverses of Trigonometric Functions and Their Reciprocal Functions

If x ∈0, π an...

Question

If x $\in (0, π)$ and $s i n x . c o s^{3} x > c o s x . s i n^{3} x$ then complete set of values of x is

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$x\in\left (0,~\frac{\pi}{4} \right )$

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Solution

The correct option is A

$s i n x . c o s^{3} x > c o s x . s i n^{3} x$

$\Rightarrow$ $s i n x . c o s x (c o s^{2} x - s i n^{2} x) > 0$

$\Rightarrow$ $s i n x c o s x c o s 2 x > 0$

$∴ x \in (0, \frac{π}{4}) U (\frac{π}{2}, \frac{3 π}{4})$

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