# Question b8301

$\sin \frac{\frac{\pi}{4} - x}{\sin} \left(\frac{\pi}{4} + x\right)$
$\frac{\cos 2 x}{1 + \sin 2 x} = \frac{{\cos}^{2} x - {\sin}^{2} x}{{\cos}^{2} x + {\sin}^{2} x + 2 \sin x \cos x} = \frac{\left(\cos x - \sin x\right) \left(\cos x + \sin x\right)}{\cos x + \sin x} ^ 2 = \frac{\cos x - \sin x}{\cos x + \sin x}$
Divide numerator and denominator by$\sqrt{2}$ and use $\sin \left(\frac{\pi}{4}\right) = \cos \left(\frac{\pi}{4}\right) = \frac{1}{\sqrt{2}}$
A simplified form is $\sin \frac{\frac{\pi}{4} - x}{\sin} \left(\frac{\pi}{4} + x\right)$.