смотреть во вложения!!!

Решите задачу:

$\frac{\sqrt{1-2sin\frac{\alpha}{2}cos\frac{\alpha}{2}}}{cos\alpha}(sin\frac{\alpha}{2}+cos\frac{\alpha}{2})=\frac{\sqrt{(1-2sin\frac{\alpha}{2}cos\frac{\alpha}{2})(sin\frac{\alpha}{2}+cos\frac{\alpha}{2})^2}}{cos\alpha}=\\\ =\frac{\sqrt{(1-2sin\frac{\alpha}{2}cos\frac{\alpha}{2})(sin^2\frac{\alpha}{2}+2sin\frac{\alpha}{2}cos\frac{\alpha}{2}+cos^2\frac{\alpha}{2})^2}}{cos\alpha}=\\\ =\frac{\sqrt{(1-sin\alpha)(1+sin\alpha)}}{cos\alpha}=\frac{\sqrt{1-sin^2\alpha}}{cos\alpha}=$

$\frac{\sqrt{cos^2{\alpha}}}{cos\alpha}=\frac{cos\alpha}{cos\alpha}=1$