Question

compute
cosec(13pie/12)

Answer 1

Answer:

$- \sqrt{2} (\sqrt{3} +1)$

Step-by-step explanation:

 [$cosec(\frac{13\pi }{12}) \\= cosec (\pi + \frac{\pi }{12})\\= - cosec \frac{\pi}{12} \\\\= - cosec \ 15\°\\= - \sqrt{1 + cot^{2} \ 15\° } \\= - \sqrt{1 + (2 + \sqrt{3} )^{2} } \ \ \ Since \ cot\ 15\° = 2 + \sqrt{3} \\ = - \sqrt{1 + 4 + 3 + 4\sqrt{3} } \\= - \sqrt{8 + 4\sqrt{3} } \\= - \sqrt{8 + 2\sqrt{12} } \\= - \sqrt{6 + 2 + 2\sqrt{6}\sqrt{2} } \\= - \sqrt{ (\sqrt{6} + \sqrt{2} )^{2} } \\\\= - (\sqrt{6} + \sqrt{2}) \\\\= -\sqrt{6} - \sqrt{2}\\= -\sqrt{2} (\sqrt{3} + 1)$