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Question

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

A
0
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B
1
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C
12
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D
none of these
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Solution

The correct option is A 12
Let y=cosπ11+cos3π11+cos5π11+cos7π11+cos9π11
y=(2cosπ11sinπ11)+(2cos3π11sinπ11)+(2cos5π11sinπ11)+(2cos7π11sinπ11)+(2cos9π11sinπ11)2sinπ11
y=sin2π11+sin4π11sin2π11+sin6π11sin4π11+sin8π11sin6π11+sin10π11sin8π112sinπ11
because 2cosAsinB=sin(A+B)sin(AB)
y=sin10π112sinπ11=sin10π112sin(ππ11)=12
Ans: C

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