Prove that the tangent of an acute angle is greater than the sine of this angle.

As you know, the tangent is the ratio of the opposite leg to the adjacent leg, and the sinus is the ratio of the opposite leg to the hypotenuse. If we take an acute angle (standard in solutions) equal to 45 degrees, then sin45 = √2 / 2 = 1.4 / 2 = 0.7, while tg45 = 1. This means that in this case the tangent is greater than the sine of the same angle.
But, if we were given an arbitrary angle, the value of which we do not know, then the tangent can be written as tga = sina / cosa. Divide the sine by the value, then it will become less than tga.