Question

Найдите значение выражения с объяснениями

Answer 1

$\cos^2{(\frac{\pi}{4}-\alpha)}=(\cos{\frac{\pi}{4}}\cos{\alpha}+\sin{\frac{\pi}{4}}\sin{\alpha})^2=(\frac{\cos{\alpha}}{\sqrt{2}}+\frac{\sin{\alpha}}{\sqrt{2}})^2=(\frac{\cos{\alpha}+\sin{\alpha}}{\sqrt{2}})^2=\\=\frac{(\cos{\alpha}+\sin{\alpha})^2}{2}\\\frac{(\cos{\alpha}+\sin{\alpha})^2}{\frac{(\cos{\alpha}+\sin{\alpha})^2}{2}}=(\cos{\alpha}+\sin{\alpha})^2*\frac{2}{(\cos{\alpha}+\sin{\alpha})^2}=2$

Ответ: 2