Evaluate the limit using special trigonometric limit of cosine

The video tutorial explains how to solve the limit of (1-cos(X))/X as X approaches 0. It begins by stating the problem and then uses properties of limits to simplify the expression by taking constants outside the limit. The instructor calculates the limit, initially making a mistake, but then corrects it to show that the limit equals 0. The session concludes with encouragement to try more challenging problems.

What is the final result of the limit discussed in the text?

What did the teacher suggest after discussing the limit?