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3.Trigonometrical Ratios, Functions and Identities
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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
A
$- 1/2$
B
$1/2$
C
$1$
D
$0$
Solution
$put \frac{\pi}{28} = x$
$T_1$ $= \frac{{\cos \,2\,x}}{{\sin \,3\,x}}$
$= \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.
Standard 11
Mathematics
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