Mathematics Question on limits of trigonometric functions

Question

$\displaystyle\lim _{x \rightarrow \frac{\pi}{4}} \frac{8 \sqrt{2}-(\cos x+\sin x)^7}{\sqrt{2}-\sqrt{2} \sin 2 x}$ is equal to

Answer 1

sinx+cosx=t
1+sin2x=t2
sin2x=t2−1
t→2lim2−2(t2−1)82−t7
t→2lim22−2t282−t7 (L-Hospital Rule)
t→2lim−22t−7t6=t→2lim227×t5
=227×(2)5=14