[tex]\frac{1+2sin\alpha cos\alpha}{(sin\alpha+cos \alpha)^{2}}=\frac{1+2sin\alpha cos\alpha}{sin^{2}\alpha + 2sin\alpha cos\alpha + cos^{2}\alpha}=\frac{1+2sin\alpha cos\alpha}{1+2sin\alpha cos\alpha} =1[/tex]
[tex]c.n.w.[/tex]
Wyjaśnienie:
[tex]sin^{2}\alpha + cos^{2}\alpha = 1[/tex]
