Bonsoir,
[tex]\dfrac{1}{\sqrt{2}}\times\left(\cos(2\theta)+\sin(2\theta)\right)\\\\=\dfrac{\cos(2\theta)}{\sqrt{2}}+\dfrac{\sin(2\theta)}{\sqrt{2}}\\\\\\=\dfrac{\sqrt{2}\cos(2\theta)}{2}+\dfrac{\sqrt{2}\sin(2\theta)}{2}\\\\=\dfrac{\sqrt{2}}{2}\cos(2\theta)+\dfrac{\sqrt{2}}{2}\sin(2\theta)\\\\=\sin\left(\dfrac{\pi}{4}\right)\cos(2\theta)+\cos\left(\dfrac{\pi}{4}\right)\sin(2\theta)\\\\\\=\sin\left(\dfrac{\pi}{4}+2\theta\right)[/tex]
