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Question Number 128582 by john_santu last updated on 08/Jan/21
  cot^2 ((π/7))+cot^2 (((2π)/7))+cot^2 (((3π)/7))=?
cot2(π7)+cot2(2π7)+cot2(3π7)=?
Answered by liberty last updated on 08/Jan/21
 T = cot^2 ((π/7))+cot^2 (((2π)/7))+cot^2 (((3π)/7))   T=csc^2 ((π/7))+csc^2 (((2π)/7))+csc^2 (((3π)/7))−3   T= (1/(sin^2 ((π/7))))+(1/(sin^2 (((2π)/7))))+(1/(sin^2 (((3π)/7))))−3   T = (2/(1−cos (((2π)/7))))+(2/(1−cos (((4π)/7))))+(2/(1−cos (((6π)/7))))−3   T= (2/(1+cos ((π/7))))+(2/(1+cos (((3π)/7))))+(2/(1+cos (((5π)/7))))−3   T= ((2 [ (1+cos (π/7))(1+cos ((3π)/7))+(1+cos (π/7))(1+cos ((5π)/7))+(1+cos ((3π)/7))(1+cos ((5π)/7)) ])/((1+cos (π/7))(1+cos ((3π)/7))(1+cos ((5π)/7))))−3   T= ((2[1+cos (π/7)+cos ((3π)/7)+cos (π/7).cos ((3π)/7)+1+cos (π/7)+cos ((5π)/7)+cos (π/7).cos ((5π)/7)+1+cos ((3π)/7)+cos ((5π)/7)+cos ((3π)/7).cos ((5π)/7) ])/((1+cos ((5π)/7))(1+cos (π/7)+cos ((3π)/7)+cos (π/7).cos ((3π)/7))))−3  T = 8−3 = 5
T=cot2(π7)+cot2(2π7)+cot2(3π7)T=csc2(π7)+csc2(2π7)+csc2(3π7)3T=1sin2(π7)+1sin2(2π7)+1sin2(3π7)3T=21cos(2π7)+21cos(4π7)+21cos(6π7)3T=21+cos(π7)+21+cos(3π7)+21+cos(5π7)3T=2[(1+cosπ7)(1+cos3π7)+(1+cosπ7)(1+cos5π7)+(1+cos3π7)(1+cos5π7)](1+cosπ7)(1+cos3π7)(1+cos5π7)3T=2[1+cosπ7+cos3π7+cosπ7.cos3π7+1+cosπ7+cos5π7+cosπ7.cos5π7+1+cos3π7+cos5π7+cos3π7.cos5π7](1+cos5π7)(1+cosπ7+cos3π7+cosπ7.cos3π7)3T=83=5
Commented by Study last updated on 10/Jan/21
why 1−cos(((2π)/7))=1+cos((π/7))  1−cos(((4π)/7))=1+cos(((3π)/7))  1−cos((6π)/7)=1+cos((5π)/7) ???
why1cos(2π7)=1+cos(π7)1cos(4π7)=1+cos(3π7)1cos6π7=1+cos5π7???
Commented by liberty last updated on 13/Jan/21
1−cos (((6π)/7))=1+cos ((π/7))  1−cos (((4π)/( 7)))=1+cos (((3π)/7))  1−cos (((2π)/7))=1+cos (((5π)/7))
1cos(6π7)=1+cos(π7)1cos(4π7)=1+cos(3π7)1cos(2π7)=1+cos(5π7)
Commented by Adel last updated on 14/Jan/21
  Please help improve this article or section by expanding it
Please help improve this article or section by expanding it
Commented by Adel last updated on 14/Jan/21
1−cos (((2π)/7))=1−cos (π−((5π)/7))=1−(−cos ((5π)/7))=1+cos (((5π)/7))    1−cos (((4π)/7))=1−cos (π−((5π)/7))=1−{−cos (((5π)/7))}=1+cos (((5π)/7))    1−cos (((6π)/7))=1−cos (π−(π/7))=1−{−cos ((π/7))}=1+cos ((π/7))    Solve  Adil Rahman Danish
1cos(2π7)=1cos(π5π7)=1(cos5π7)=1+cos(5π7)1cos(4π7)=1cos(π5π7)=1{cos(5π7)}=1+cos(5π7)1cos(6π7)=1cos(ππ7)=1{cos(π7)}=1+cos(π7)SolveAdilRahmanDanish

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