Math CentralQuandaries & Queries


Question from isaiah, a student:

i'm having trouble proving 1-tanx / 1+tanx = 1-sin2x / cos2x, can anyone help me from going crazy?


I would work with the left side, (1 - tan x)/(1 + tan x). Write each tan x as sin x/cos x and simplify. Multiply the numerator and denominator of the resulting fraction by (1 - cos x) and simplify. Remember that

sin 2x = 2 sin x cos x and
cos 2x = cos2 x - sin2 x


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