Question

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Answer 1

$x = \frac{\csc(\alpha)\:-\:\sin(\alpha)}{\sec(\alpha)\:-\:\cos(\alpha)}$

$x = \frac{\frac{1}{\sin(\alpha)}-\:\sin(\alpha)}{\frac{1}{\cos(\alpha)}\:-\:\cos(\alpha)}$

$x = \frac{ \frac{1\:-\:\sin^{2}(\alpha)}{\sin(\alpha)}}{\frac{1\:- \:\cos^{2}(\alpha)}{\cos(\alpha)}}$

$x = \frac{\cos^{2}(\alpha)}{\sin(\alpha)}\frac{\cos(\alpha)}{ \sin^{2}(\alpha)}$

$x = \cot^3(\alpha)$

$\alpha = \cos^{-1}(\frac{1}{2})$

$\alpha = \frac{\pi}{3}$

$x = \cot^3(\frac{\pi}{3})$

$x = (\frac{\sqrt{3} }{3})^{3}$

$x = \frac{\sqrt{3}}{9}$