Solution to this signal even or odd
This function is neither even nor odd:

$$x(-t)=\cos(-t)+\sin(-t)\cos^2(-t)=\cos(t)-\sin(t)\cos^2(t)$$

And since

$$x(-t)\neq x(t)\quad\text{and}\quad x(-t)\neq -x(t)$$

this function is neither even nor odd.