1)
(sin@ + cos@)^2 = sin^2@ + 2sin@cos@ + cos^2@ = sin^2@ + cos^2@ + 2sin@cos@ = 1 + 2sin@cos@

2sin@cos@ = sin2@ (double angle formula)
(sin@ + cos@)^2 - 2sin@cos@ = 1 + sin2@

2)
[tex] \frac{2 - \sin{}^{2}\alpha - \cos{}^{2}\alpha}{3\sin{}^{2}\alpha + 3\cos{}^{2}\alpha} [/tex]

[tex] \frac{2 - (\sin{}^{2}\alpha + \cos{}^{2}\alpha)}{3(\sin{}^{2}\alpha + \cos{}^{2}\alpha)} [/tex]

Since sin^2@ + cos^2@ = 1,

[tex] \frac{2 - 1}{3(1)} [/tex] = [tex] \frac{1}{3} [/tex]