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Solve the half-trigonometric equation

Source: Kazakhstan NMO 2005 (Final round) P5

December 16, 2014
trigonometryalgebra proposedalgebra

Problem Statement

Solve equation 212−2∣x∣=∣tan⁡x+12∣+∣tan⁡x−12∣2^{\tfrac{1}{2}-2|x|} = \left| {\tan x + \frac{1}{2}} \right| + \left| {\tan x - \frac{1}{2}} \right|
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