The exact value of cos frac{{2pi }}{{28}},cos | vedclass

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Question

$put \frac{\pi}{28} = x$

$T_1$ $= \frac{{\cos \,2\,x}}{{\sin \,3\,x}}$ 

$= \frac{{\cos \,2\,x\,\,\sin \,x}}{{\sin \,3\,x\,\,\sin \,x}} $

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Vedclass · Answer

$put \frac{\pi}{28} = x$

$T_1$ $= \frac{{\cos \,2\,x}}{{\sin \,3\,x}}$ 

$= \frac{{\cos \,2\,x\,\,\sin \,x}}{{\sin \,3\,x\,\,\sin \,x}} $

$= \frac{1}{2}\left[ {\frac{{\sin \,3x\, - \,\sin \,x}}{{\sin \,3x\,\,\sin \,x}}} \right] $

$= \frac{1}{2}\left[ {\cos \,ecx\, - \,\cos \,ec\,3x} \right]$ etc.

The exact value of $\cos \frac{{2\pi }}{{28}}\,\cos ec\frac{{3\pi }}{{28}}\, + \,\cos \frac{{6\pi }}{{28}}\,\cos ec\frac{{9\pi }}{{28}} + \cos \frac{{18\pi }}{{28}}\cos ec\frac{{27\pi }}{{28}}$ is equal to

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