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Questions  

The value of sin π18sin5π18sin7π18, is

a
1/2
b
1/4
c
1/8
d
1/16

detailed solution

Correct option is C

We havesin⁡π18sin⁡5π18sin⁡7π18=cos⁡π2−π18cos⁡π2−5π18cos⁡π2−7π18=cos⁡8π18cos⁡4π182π8cos⁡2π8=cos⁡π9cos⁡2π9cos⁡4π9=sin⁡23⋅π/9231sin⁡π/9=123=18

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