Show that Sec2A - Tan2A = (CosA-SinA)/(CosA+SinA)

Sec2A - Tan2A Definition of Sec and Tan = 1/Cos2A - Sin2A/Cos2A Combining Fractions = (1 - Sin2A) / (Cos2A) Apply Double Angle Formula = (1 - 2SinACosA) / (Cos²A - Sin²A) Make use of 1 = Cos²x + Sin²x and Difference of two squares = (Cos²A + Sin²A - 2SinACosA) / (CosA + SinA)(CosA - SinA) Factorise the numerator = (CosA - SinA)² / (CosA + SinA)(CosA - SinA) Divide out by (CosA - SinA) = (CosA - SinA) / (CosA + SinA)