It is posible for x to be equal to sinx ?

Yes, it is possible for x = 0. But let's prove
it!

We'll have to solve the equation x - sin x =
0.

The equation is a transcedental one, so we'll have to
differentiate the function f.

Before differentiating, we'll
check if the function is continuous. Because f(x) is formed by elementary functions as
the linear one, x , and the trigonometric function, sin x, f(x) is a continuous
function.

We'll differentiate
f(x).

df/dx =
1-cosx

We notice that f(x) is a monotone increasing
function.

( -1<cosx<1), so the difference 1
-cos x>0 =>f(x)>0, so f(x) is an
injection.

We can also do a very simple
calculus:

f(0)=0-sin0=0-0=0.

Because
f(x) is an one-to-one, x=0 is the only solution for the equation 
x-sinx=0.

So, yes, x = sin x, for x =
0.