Buktikan bahwa: (sin alfa + cos alfa) ²+ ( sin alfa-cos alfa) ²= 2

[tex]( \sin( \alpha ) + \cos( \alpha ) )^{2} + {( \sin( \alpha ) - \cos( \alpha )) }^{2} = 2 \\ {sin}^{2} ( \alpha ) + {cos }^{2} ( \alpha ) + 2 \sin( \alpha ) \cos( \alpha ) + ( {sin}^{2} ( \alpha ) + {cos}^{2} ( \alpha ) - 2 \sin( \alpha ) \cos( \alpha )) = 2 \\ 1 + 2 \sin( \alpha ) \cos( \alpha ) + (1 - 2 \sin( \alpha ) \cos( \alpha ) ) = 2 \\ 2 = 2 \: (terbukti)[/tex]