# SOLUTION: (cos^3(A/2)-3cot(A/2))/(3cot^2(A/2)-1)=cot(A)

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 Algebra: Trigonometry Solvers Lessons Answers archive Quiz In Depth

 Question 41125: (cos^3(A/2)-3cot(A/2))/(3cot^2(A/2)-1)=cot(A)Answer by venugopalramana(3286)   (Show Source): You can put this solution on YOUR website!(cos^3(A/2)-3cot(A/2))/(3cot^2(A/2)-1)=cot(A) ANGLES ON LHS ARE A/3 AND NOT A/2 IF YOU KNOW TAN(3X) FORMULA THIS IS A STRAIGHT APPLICATION TAN(3X)={3TAN(X)-TAN^3(X)}/{1-3TAN^2(X)} HENCE COT(3X)={1-3TAN^2(X)}/{3TAN(X)-TAN^3(X)}...PUT TAN(X)=1/COT(X)...WEB GET COT(3X)={COT^2(X)-3}COT^3(X)/{3COT^2(X)-1}COT^2(X) ={COT^3(X)-3COT(X)}/{3COT^2(X)-1} PUT 3X=A...WE GET COT(A)={COT^(A/3)-3COT(A/3)}/{3COT^2(A/3)-1} IF YOU DONT KNOW TAN(3X) FORMULA...THEN WRITE TAN(3X)=TAN(2X+X)={TAN(2X)+TAN(X)}/{1-TAN(2X)TAN(X)...AGAIN EXPAND TAN(2X)=2TAN(X)/(1-TAN^2(X)....ETC...