DOUBLE SUBSTITUTION IN THE PROOF AND IN SOLVING TRIGONOMETRIC INEQUALITIES

Abstract

The double substitution method for solving equations, inequalities and problems with parameters is almost not presented in the educational literature, although for some types of these problems it turns out to be more convenient in comparison with other methods. This work continues a series of publications on applications of double substitution. The features and advantages of the method have been described in previous works using examples of trigonometric and irrational equations. Double substitution gives additional advantages when solving inequalities and problems with parameters, since it significantly expands the possibilities of using graphical methods. The researchers consider examples of double substitution in the proof and solution of trigonometric inequalities, and describe some types of inequalities in which double substitution is appropriate.