15.6. If $\frac{1}{2} \sin ^{2} x+C=-\frac{1}{4} \cos 2 x$ is an identity, what is the value of $C$ ?
15.6. $-\frac{1}{4}$
Since the equation is an identity, it is true for all $x$ in the domain (which is $\mathbb{R}$ ) of the equation. To find $C$, we only set a particular value of $x$. For convenience, when we let $x=0$, we have $C=-\frac{1}{4}$.