If the area of the region bounded by y = cos x, y = sin x, x = \(\frac{\pi}{4}\) and x = π is bisected by the line x = a, then \(\sin \left(\text{a}+\frac{\pi}{4}\right)\) =
1
\(\frac{\sqrt{2}}{2+\sqrt{2}}\)
2
\(\frac{\sqrt{3}+1}{2}\)
3
\(\frac{\sqrt{2}−1}{2 \sqrt{2}}\)
4
\(\frac{\sqrt{3}+1}{2 \sqrt{2}}\)