Prove that (1-cos2x)/sin(2x) = tan(x) where x ≠ nπ/2
Starting from the left hand side we can substitute the sin and cos sum and difference formulas. These are sin(A+B) = sinAcosB + cosAsinBand cos(A+B) = cosAcosB - sinAsinBBecause x = A = B when substituted these formulae become:sin(2x) = sin(x)cos(x) + sin(x)cos(x) = 2sin(x)cos(x)cos(2x) = cos2(x) - sin2(x) When substituted into the question(1-cos2(x) + sin2(x))/2sin(x)cos(x) = 2sin2(x)/2sin(x)cos(x) = sin(x)/cos(x) = tan(x)This is as required
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