Here I would like to answer this question graphically,
this is y=sin(X) graph
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
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