Question

Fie alfa astfel incat Sin alfa + cos alfa = 1/3. Calculati sin 2 alfa

Answer 1

$sin ( \alpha ) + cos( \alpha ) = \frac{1}{3} = > \\ (sin ( \alpha ) \: + \: cos( \alpha ))^{2} = \frac{1}{9} \\ 1 + \: 2 \: sin ( \alpha )cos( \alpha ) \: = \frac{1}{9} \\ sin(2\alpha) = \frac{ - 8}{9}$