I'm kind of confused with these
is $\displaystyle sin^2x$ and $\displaystyle sinx^2$ the same?
if they are they both can be written as $\displaystyle (sinx)^2$ ?
They're not. Unfortunately, we cannot make every write mathematics correctly (I've tried!) so we have to guess what they really mean!
$\displaystyle sin^2(x)= (sin(x))^2$ but $\displaystyle sin(x^2)$ is different.
For example, if x= 1 then sin(x)= sin(1)= 0.84147, approximately, so that $\displaystyle sin^2(1)= (sin(1))^2= (0.84147)^2= 0.70807$ while [tex]sin(x^2)= sin(1)= 0.84147[tex].
I did warn you not to use $\displaystyle \sin$ by itself!
It is a function notation. As such, it must be written in function notation: $\displaystyle \sin(x)$.
It is quite often the case that the notation $\displaystyle f^n(x)$ is used in place of $\displaystyle \left(f(x)\right)^n$.
In several computer algebra systems, one must use $\displaystyle \left(\sin(x)\right)^2$ for they will not recognize $\displaystyle \sin^2(x)$.
But again, reread my post. I told to use () with the sine function.