17.52 USE problems
Condition: Solve the following equation by introducing an auxiliary argument. \[ \cos 3 x-\sin 5 x=\sqrt{3}(\cos 5 x-\sin 3 x) \] Note. Write the equation as \( \cos 3 x+\sqrt{3} \sin 3 x=\sin 5 x+\sqrt{3} \cos 5 x \). Apply the auxiliary argument method to the left and right sides of this equation.
Problems of the USE (Unified State Exam) - equations and inequalities in terms of a parameter, solved both by algebraic methods and geometric ones.