Answer
$\dfrac{1}{2}$
Work Step by Step
Note that, $\lim\limits_{x \to a}\sin x=\sin a$ for all real numbers $a$. Using this along with our limit laws, we get
$\lim\limits_{x \to \frac{\pi}{4}}\sin^2 x=\left(\sin\left(\frac{\pi}{4}\right)\right)^2=\left(\dfrac{1}{\sqrt{2}}\right)^2=\dfrac{1}{2}.$
