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Questions  

The value of cosπ15cos2π15cos3π15cos4π15cos5π15cos6π15cos7π15, is

a
126
b
127
c
128
d
none of these

detailed solution

Correct option is B

We have,cos⁡π15cos⁡2π15cos⁡3π15cos⁡4π15cos⁡5π15cos⁡5π15cos⁡6π15cos⁡7π15=cos⁡π15cos⁡2π15cos⁡4π15cos⁡7π15×cos⁡3π15cos⁡6π15×cos⁡5π15=cos⁡π15cos⁡2π15cos⁡4π15cos⁡π−8π15cos⁡3π15cos⁡6π15                                                                                   ×cos⁡π3=−cos⁡π15cos⁡2π15cos⁡4π15cos⁡8π15×cos⁡3π15cos⁡6π15×12=sin⁡24×π1524sin⁡π15×sin⁡22×3π1522sin⁡3π15×12=−sin⁡16π1516sin⁡π15×sin⁡12π154sin⁡3π15×12=116×14×12=127

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