The value of cosπ11+cos3π11+cos5π11+cos7π11+cos9π11

cosπ11+cos3π11+cos5π11+cos7π11+cos9π11 =sin5π11sinπ11.cos(π11+9π112) =sin5π11.cos5π11sinπ11=12sin10π11sinπ11=12

The value of cosπ11+cos3π11+cos5π11+cos7π11+cos9π11

cosπ11+cos3π11+cos5π11+cos7π11+cos9π11 =sin5π11sinπ11.cos(π11+9π112) =sin5π11.cos5π11sinπ11=12sin10π11sinπ11=12

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The value of $\cos \frac{π}{11} + \cos \frac{3 π}{11} + \cos \frac{5 π}{11} + \cos \frac{7 π}{11} + \cos \frac{9 π}{11}$

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$\frac{3}{4}$

$\frac{2}{9}$

$\frac{1}{2}$

answer is C.

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Detailed Solution

$\cos \frac{π}{11} + \cos \frac{3 π}{11} + \cos \frac{5 π}{11} + \cos \frac{7 π}{11} + \cos \frac{9 π}{11} = \frac{\sin \frac{5 π}{11}}{\sin \frac{π}{11}} . \cos (\frac{\frac{π}{11} + \frac{9 π}{11}}{2}) = \frac{\sin \frac{5 π}{11} . \cos \frac{5 π}{11}}{\sin \frac{π}{11}} = \frac{\frac{1}{2} \sin \frac{10 π}{11}}{\sin \frac{π}{11}} = \frac{1}{2}$