Помогите доказать тождество 1+sina=2cos^2(45градусов - a/2)

[latex]1+sin\alpha=2cos^{2}(45^{0}-\frac{\alpha}{2}) \\1+sin\alpha=1+cos(90^{0}-\alpha)=sin^{2}(45^{0}-\frac{\alpha}{2})+cos^{2}(45^{0}-\frac{\alpha}{2})+\\+cos^{2}(45^{0}-\frac{\alpha}{2})-sin^{2}(45^{0}-\frac{\alpha}{2})=2cos^{2}(45^{0}-\frac{\alpha}{2}) [/latex] Ч.Т.Д)))))))))))