cosec frac{pi }{{18}} - sqrt 3 ,se | vedclass

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Question

$\frac{1}{{\sin \pi /18}}\,\, - \,\,\frac{{\sqrt 3 }}{{\cos \pi /18}}$ $=$$\frac{{2\,\left[ {\frac{1}{2}\cos \frac{\pi }{{18}}\, - \,\frac{{\sqrt 3 }}

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$\frac{1}{{\sin \pi /18}}\,\, - \,\,\frac{{\sqrt 3 }}{{\cos \pi /18}}$ $=$$\frac{{2\,\left[ {\frac{1}{2}\cos \frac{\pi }{{18}}\, - \,\frac{{\sqrt 3 }}{2}\,\,\sin \frac{\pi }{{18}}} \right]}}{{\frac{{\sin \frac{\pi }{9}}}{2}}}$

$=$$\frac{{4\left[ {\sin \frac{\pi }{6}\,\,\cos \frac{\pi }{{18}}\,\, - \,\,\cos \frac{\pi }{6}\,\,\sin \frac{\pi }{{18}}} \right]}}{{\sin \frac{\pi }{9}}}$ $= 4$

$cosec \frac{\pi }{{18}} - \sqrt 3 \,sec\, \frac{\pi }{{18}}$ =

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