Can you show that the equation 3x cos 2x + (sinx) ² = 0 has at least five solutions on the interval [-pi,pi]?

Answer 1

The easiest way to do this is to graph the equation and you will see immediately that the statement is correct.

Otherwise, I would try to use the identity cos 2x = cos²x - sin²x to eliminate either the use of cos 2x or of sin²x to solve the equation and I am not sure which substitution will get the easier result.