삼각함수 극한

$\displaystyle \frac{\pi}{2} - x = t$라 하면 $\displaystyle x \rightarrow \frac{\pi}{2}$일 때, $t \rightarrow 0$이므로 $\displaystyle \lim\limits _{x \rightarrow \frac{\pi}{2}} \frac{\cos ^{2} x}{( 2 x - \pi ) ^{2}}$$\displaystyle = \lim\limits _{t\rightarrow 0} \frac{\cos ^{2} \left( \frac{\pi}{2} - t \right)}{( - 2 t ) ^{2}}$ $\displaystyle = \lim\limits _{t\rightarrow 0} \frac{\sin ^{2} t}{4 t ^{2}}$$\displaystyle = \frac{1}{4} \lim\limits _{t\rightarrow 0} \left( \frac{\sin t}{t} \right) ^{2}$$\displaystyle = \frac{1}{4}$