2. Найти cosa, tga, sin2a, cos2a, если sin a = -12/37 и π<a <3π/2 ;

$$cos^2a = 1 - sin^2a$$

$$cosa = -\sqrt{1 - sin^2a} = -\sqrt{1 - (-\frac{12}{37})^2} = -\sqrt{1 - \frac{144}{1369}} = -\sqrt{\frac{1369 - 144}{1369}} = -\sqrt{\frac{1225}{1369}} = -\frac{35}{37}$$

$$tga = \frac{sina}{cosa} = \frac{-\frac{12}{37}}{-\frac{35}{37}} = \frac{12}{35}$$

$$sin2a = 2sinacosa = 2 \cdot (-\frac{12}{37}) \cdot (-\frac{35}{37}) = \frac{2 \cdot 12 \cdot 35}{37^2} = \frac{840}{1369}$$

$$cos2a = cos^2a - sin^2a = (-\frac{35}{37})^2 - (-\frac{12}{37})^2 = \frac{1225}{1369} - \frac{144}{1369} = \frac{1225 - 144}{1369} = \frac{1081}{1369}$$

Ответ: $$cosa = -\frac{35}{37}$$, $$tga = \frac{12}{35}$$, $$sin2a = \frac{840}{1369}$$, $$cos2a = \frac{1081}{1369}$$