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rinik, September 20, 2013
Posted September 20, 2013
the answer is tan(pi/7)
So here you would use the double angle formulas. So sin(2A)=2sinAcosA and cos(2A) = 2(cosA)^2-1 - you want to use this form of cos(2A) as you want everything to cancel out in the denominator. So, when you simplify sin(2pi/7)/(1-cos(2pi/7), you get 2sin(pi/7)cos(pi/7)/2(cos(pi/7))^2 = sin(pi/7)/cos(pi/7) = tan(pi/7).
If you want a breakdown of the double angle forumlas, I found this while trying to solve the problem:
Thanks. I was revising and I didn't notice that I can use that