Explicație pas cu pas:
[tex]{ \sin}^{2}a + { \cos}^{2}a = 1 \iff { \sin}^{2}a = 1 - { \cos}^{2}a \\ [/tex]
[tex]{ \sin}^{2}a = 1 - {\Big( - \frac{5}{13}\Big)}^{2} = 1 - \frac{25}{169} = \frac{144}{169} \\ [/tex]
[tex]a \in \Big( \frac{\pi}{2} ;\pi\Big) \implies \: cadranul \: 2 \\ [/tex]
[tex]\implies \bf \sin a = \frac{12}{13} \\ [/tex]
[tex]\sin(2a) = 2 \sin a \cdot \cos a = 2 \cdot \frac{12}{13} \cdot \Big( - \frac{5}{13}\Big) \\ \implies \bf \sin(2a) = - \frac{120}{169} [/tex]
[tex]\cos(2a) = 1 - 2\sin^{2} (a) = 1 - 2 \times \frac{144}{169} = \frac{169 - 288}{169} \\ \implies \bf \cos(2a) = - \frac{119}{169} [/tex]
