Question Number 100806 by I want to learn more last updated on 28/Jun/20

Commented byI want to learn more last updated on 28/Jun/20

33  sir.

Commented byjohn santu last updated on 28/Jun/20

tan ^2 (((2π)/9))+tan ^2 (((4π)/9))+tan ^2 (((8π)/9))=33

Commented byI want to learn more last updated on 28/Jun/20

Workings sir. Please

Answered by MJS last updated on 28/Jun/20

put tan^2  x =t  ⇒  t+((4t)/((t−1)^2 ))+((16t(t−1)^2 )/((t^2 −6t+1)^2 ))=33  ⇒  t^7 −47t^6 +545t^5 −2291t^4 +3611t^3 −2205t^2 +483t−33=0  (t^4 −14t^3 +56t^2 −62t+11)(t^3 −33t^2 +27t−3)=0  now solve this approximately or exactly,  for the first factor the exact solution is not  useable.  for 0≤x<(π/3) it leads to   { ((x_1 =π/9)),((x_2 =2π/9)),((x_3 =4π/9)) :} from the 3^(rd) −degree−polynome   { ((x_4 ≈.436880)),((x_5 ≈.873645)),((x_6 ≈1.13059)),((x_7 ≈1.22795)) :} from tbe 4^(th) −degree−polynome  the solutions of the given equation are  x_i +2nπ and (2n+1)π−x_i  with 1≤i≤7 and n∈Z

Commented bymaths mind last updated on 28/Jun/20

nice worck sir

Commented byI want to learn more last updated on 28/Jun/20

Thanks sir