In Example 7, change the + to −.

Data from Example 7

Solve the equation cos3x cos x + sin 3x sin x = 1(0 ≤ x < 2π). The left side of this equation is of the general form cos(A − x), where A = 3x. Therefore, cos3x cos x + sin 3x sin x = cos(3x − x) = cos 2x

The original equation becomes cos2x = 1.This equation is satisfied if 2x = 0 or 2x = 2π. The solutions are x = 0 and x = π. Only through recognition of the proper trigonometric form can we readily solve this equation. We see that these solutions agree with the two values of x for which the graph of y = cos3x cos x + sin3x sin x − 1 touches the x-axis in Fig. 20.31.

Transcribed Image Text:

y 3 0 по Fig. 20.31 6 Х