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)
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