I'm going to assume the arguments are in degrees, and so we need only consider that on the interval [MATH][0^{\circ},90^{\circ})[/MATH] the tangent function is non-negative and increasing. As both products have [MATH]\tan(5^{\circ})[/MATH] as a factor, we need only consider that we must have:

[MATH]\tan(4^{\circ})<\tan(6^{\circ})[/MATH]

Which then means we must have:

[MATH]\tan(4^{\circ})\tan(5^{\circ})<\tan(5^{\circ})\tan(6^{\circ})[/MATH]