Answer
$\text{True}$
Work Step by Step
Working on the $RHS$:
$\begin{aligned}(x+1)^{2}-1 &=\left(x^{2}+2 x+1\right)-1 \\ &=x^{2}+2 x \\ &=L \ H \ S \\ \therefore L H S &=R H S \\ \text { Hence it is an Identity } \end{aligned}$
Thus, the given statement is true.
