Definite Integration

Assertion (A) $\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{(\sin x)^{\sqrt{2}} d x}{(\sin x)^{\sqrt{2}}+(\cos x)^{\sqrt{2}}}=\frac{\pi}{12}$

Reason (R) $\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{f(x) d x}{f(x)+f\left(\frac{\pi}{2}-x\right)}=\frac{\pi}{12}$