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Trigonometric Equations: Bioche Rule
This lecture covers the Bioche rule for solving rational trigonometric equations by substitutions such as z = cos x, z = sin x, z = tan x, and z = tan. It explains how to transform trigonometric equations into algebraic equations and determine solutions. Various tests of invariance are discussed, including replacing x with π+x or -x. The lecture also addresses the challenges of solving high-degree polynomial equations resulting from the substitution z = tan. Practical procedures and examples are provided to illustrate the application of the Bioche rule in solving trigonometric equations.