17.52 Use Problems

Condition: Solve the following equation by introducing an auxiliary argument. \ [\ cos 3 x- \ sin 5 x = \ sqrt {3} (\ cos 5 x- \ sin 3 x) \] indication. Write down the equation in the form \ (\ cos 3 x+\ sqrt {3} \ sin 3 x = \ sin 5 x+\ sqrt {3} \ cos 5 x \). Apply the method of introducing an auxiliary argument to the left and right parts of this equation.