The formulas used to analyze the horizontal and vertical motion of projectiles launched at an angle involve the use of which function(s)?

The quickest, easiest, and most direct way to handle that kind of motion involves the use of the sine and cosine.  But if you wanted to show off, you could do it with the secant and cosecant too.

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards