Here I would like to answer this question graphically, this is y=sin(X) graph Here blue line indicates y=x curve Red curve Indicates y= sin(x) by comparing both curves in one frame we can clearly understand the value of y-axis will become equal for a certain range. Beyond that, the value far differs as we can see from the graph. That is why we can wright sin(x)=x @ x tends to zero. conclusion hence prove lim sinx/x=1 @x tends to 0