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Question

If k=sinπ/18sin5π/18sin7π/18, then the numerical value of k is equal to

A
12
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B
14
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C
18
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D
118
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Solution

The correct option is C 18
k=sinπ/8sin5π/18sin5π/18sin7π/18
=sin10sin50sin70
=12[cos40cos60]sin70
=12cos40sin7014sin70
=14[sin110+sin30]14sin70
=14sin(18070)+14×1214sin70=18

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