I am trying to simplify \(\displaystyle{2}{\cos{{\left({6}\frac{\pi}{{7}}\right)}}}+{2}{\cos{{\left({2}\frac{\pi}{{7}}\right)}}}+{2}{\cos{{\left({4}\frac{\pi}{{7}}\right)}}}+{1}\)

monkeyman130yb

monkeyman130yb

Answered question

2022-03-29

I am trying to simplify
2cos(6π7)+2cos(2π7)+2cos(4π7)+1

Answer & Explanation

Marcos Boyer

Marcos Boyer

Beginner2022-03-30Added 12 answers

2cos(6π7)+2cos(2π7)+2cos(4π7)+1
=2(cos(6π7)+cos(4π7)+cos(2π7))+1
=2(cos(2π7)+cos(4π7)+cos(6π7)+1
=2(n=13cos(2nπ7))+1
=2(csc(π7sin(π+6π7)1)2)+1
=2(012)+1
=2(12)+1
=1+1=0

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