Answer
True.
Work Step by Step
An equation that is satisfied for every value of the variable for which both sides are defined is called an identity.
One method for solving an equation is to replace the original equation by a succession of equivalent equations until an equation with an obvious solution is obtained.
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Simplify both sides and solve for x.
$(x-1)^{2}-1=x(x-2)$
$x^{2}-2x+1-1=x^{2}-2x\qquad\quad /$ add $-x^{2}+2x$
$x^{2}-x^{2}-2x+2x+1-1=x^{2}-x^{2}-2x+2x$
$0=0$
This equation is true for every value of x. Thus, it is an identity, as are the equations equivalent to it.
The statement is true.
