As we know x.x = x²,so sin.sin = sin² but, Why sinx.sinx = sin²x not sin²x²? Please explain.
It's important to understand that sin²x is a special notation that is inconsistent with other notations, and is defined to mean (sin x)
2, that is, the square of the
result of the sine function -- which is exactly what sinx.sinx means. It goes back to a time when parentheses were not used for the argument of functions, as they typically are today, and if they wrote sin x
2, it would have been read as sin(x
2), and is entirely different.
In fact, for other functions, the notation f
2(x) would usually mean that the function is applied twice (composition): f(f(x)). The notation f
-1(x) goes with this concept.
You may find these discussions interesting:
here and
here.