There are multiple ways to do this. You just have to play around with it. Here's one possibility: Expand tan (2x) using the double angle formula tan (2x) - tan(x) = 0 (2 tan x) / (1 - tan^2 x) - tan x = 0 factor out tan x tan x ( 2/(1- tan^2 x) -1 ) = 0 convert tan^2 x to sin^2 x / cos^2 x, then multiply top and bottom of fraction by cos^2 x tan x [ (cos^2 x/(cos^2 x - sin^2 x) -1] = 0 substitute for 1 = (cos^2 x - sin^2 x)/(cos^2 x - sin^2 x) and combine the 2 terms tan x [ {2 cos^2 x - cos^2 x + sin^2 x)/ ((cos^2 x - sin^2 x) Simplify the numerator tan x [ cos^2 x + sin^2 x] / (cos^2 x - sin^2 x) tan x / (cos^2 x - sin^2 x) = 0 Use one more double angle formula, cos (2x) = cos^2 x - sin^2 x tan x / cos (2x) = 0 Or, tan x * sec (2x) = 0 This is true only when tan x = 0 or sec (2x) = 0, but sec x is never 0. So tan x = 0 when x = pi * n, for integer n.

May 21st, 2015

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