Obliczyć miary kątów ostrych

[kitty1987]

Oblicz miary kątów ostrych \(\displaystyle{ \alpha i \beta}\) , gdy:

1. \(\displaystyle{ sin ( \alpha - \beta) = \frac{ \sqrt{2} }{2}}\)
i
\(\displaystyle{ cos ( \alpha + \beta) = \frac{1}{2}}\)

2. \(\displaystyle{ tg (\alpha + \beta) = \sqrt{3}}\)
i
\(\displaystyle{ cos ( \alpha - \beta) = \frac{ \sqrt{3} }{2}}\)

[Dudas]

1.
\(\displaystyle{ \begin{cases} \alpha - \beta = \frac{\pi}{4} \\ \alpha + \beta = \frac{\pi}{3} \end{cases}}\)

2.
\(\displaystyle{ \begin{cases} \alpha + \beta = \frac{\pi}{3} \\ \alpha - \beta = \frac{\pi}{6} \end{cases}}\)