if I want to push the bowling ball in a direction which is not parallel to the lane, then I need to make a Projection on the axes (the x axis is parallel with the width of the lane and the y axis is parallel with the length of the lane) ... using the Newton's laws of motion $\sum \vec F = m \vec a$ ,when I projected the force(which is the friction force) and the acceleration I got this:
$$\ -F_x \cos(\theta) = m\cdot a_x\cdot \cos(\theta)\quad \text{ and }\ -F_y\cdot \sin(\theta) = m\cdot a_y\cdot \sin(\theta)$$
by canceling out what is similar it gave me the same relation if the ball was moving forward with no angle
$$\ -F_x = m\cdot a_x \quad \text{and} \quad \ -F_y = m\cdot a_y$$
why did I get that ?