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Question

The value of cos[12cos1cos(14π5)] is

A
cos(7π5)
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B
sin(π10)
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C
cos(2π5)
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D
cos(3π5)
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Solution

The correct options are
B sin(π10)
C cos(2π5)
D cos(3π5)

We have, 12cos1(cos(14π5))

=12cos1(cos(14π5)) ...(cos(-A)=cosA)

=12cos1(cos(3ππ5))

=12(ππ5)

=2π5


Therefore

cos(2π5)

=cos(π3π5)

=cos(3π5)


Also cos(2π5)

=sin(π22π5)

=sin(π10)



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