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Question

Find the value of cos2π10+ cos22π5+ cos23π5+ cos29π10.

A
1
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B
12
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C
32
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D
2
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Solution

The correct option is D 2
cos(9π10)=cos(ππ10)=cos(π10)
cos(2π5)=cos(π3π5)=cos(3π5)
Hence, the equation can be written as
2(cos2π10+cos23π5)
cos(3π5)=sin(π23π5)=sin(π10)
Thus the equation becomes
2(cos2π10+sin2π10)
=2

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