Prove: (1-cos(2A))/sin(2A) = tan(A)

Firstly we must lay out our double angle formulas which are required for this question: cos(2A) = 1-2sin^2(A) = 2cos^2(A)-1 sin(2A) = 2sin(A)cos(A) Working from LHS: (1-cos(2A))/sin(2A) Focusing on the denominator 1-cos(2A) = 1-(1-2sin^2(A)) = 2sin^2(A) Focusing on the numerator sin(2A) = 2sin(A)cos(A) Therefore, overall: (1-cos(2A))/sin(2A) = 2sin^2(A)/2sin(A)cos(A) = 2*sin(A)sin(A) / 2sin(A)*cos(A) = sin(A)/cos(A) = tan(A) AS REQUIRED