Compute: Cosec(13π/12)

cosec (\frac{13 π}{12}) = cosec (π + \frac{π}{12}) = - cosec (\frac{π}{12}) = - cosec 15 ° = - \frac{1}{\sin 15 °} Now, \sin 15 ° = \sin (45 ° - 30 °) = \sin 45 ° \times \cos 30 ° - \cos 45 ° \times \sin 30 ° = \frac{1}{\sqrt{2}} \times \frac{\sqrt{3}}{2} - \frac{1}{\sqrt{2}} \times \frac{1}{2} = \frac{\sqrt{3} - 1}{2 \sqrt{2}} Now, cosec (\frac{13 π}{12}) = - \frac{1}{\sin 15 °} = \frac{2 \sqrt{2}}{1 - \sqrt{3}} \times \frac{1 + \sqrt{3}}{1 + \sqrt{3}} = \frac{2 \sqrt{2} + 2 \sqrt{6}}{- 2} = - \sqrt{2} - \sqrt{6}

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