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Question

If sin2π10+sin22π5+sin23π5+sin23π5+sin29π10=m.Find m

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Solution

sin2(π10)+sin2(2π5)+sin2(3π5)+sin2(9π10)=morm=sin2(π10)+sin2(9π10)+sin2(2π5)+sin2(3π5)=sin2(π10)+sin2π(π10)+sin2(2π5)+sin2π(π10)=sin2(π10)+cos2(π10)+sin2(2π5)+cos2(2π5)=1+1=2


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