Answer
$3\sqrt 2 -1 $
Work Step by Step
The point of intersection can be computed as: $\dfrac{\sin x}{\cos x}=1 \\ \tan x=1$
The area $(A)$ can be calculated as:
$A=\int_{0}^{\pi/4} [\cos x -\sin x] \ dx +\int_{\pi/4}^{5 \pi/4} [\sin x -\cos x] \ dx \\= [\sin x+\cos x]_{0}^{\pi/4}+[-\cos x -\cos x]_{\pi/4}^{5 \pi/4}\\=\sqrt 2-1 +\sqrt 2+\sqrt 2 \\=3\sqrt 2 -1 $
