#### Answer

The statement is false. The correct statement is “A trigonometric equation with an infinite number of solutions is not an identity”.

#### Work Step by Step

Let us consider a trigonometric function $\tan \theta =\frac{1}{2}$. Clearly, it has an infinite number of solutions, but it is not an identity because $\tan \theta $ can take other values as well when changing the values of $\theta $.
Thus, it can be concluded that the statement is False.