A) -sin²a; B) sin²a; C) cos²a; D) -cos²a. tga(sinacosa + sina/cosa) – (1 + sina/cosa). A) -sin²a; B) sin²a; C) cos²a; D) -cos²a.

Преобразуем выражение: \[\begin{aligned} tga(\sin a \cos a + \frac{\sin a}{\cos a}) - (1 + \frac{\sin a}{\cos a}) &= \frac{\sin a}{\cos a} \cdot (\sin a \cos a + \frac{\sin a}{\cos a}) - (1 + \frac{\sin a}{\cos a}) \\ &= \frac{\sin^2 a \cos a}{\cos a} + \frac{\sin^2 a}{\cos^2 a} - 1 - \frac{\sin a}{\cos a} \\ &= \sin^2 a + \frac{\sin^2 a}{\cos^2 a} - 1 - \frac{\sin a}{\cos a} \\ &= \sin^2 a + \frac{\sin^2 a - \sin a \cos a - \cos^2 a}{\cos^2 a} - 1 \\ &= \sin^2 a - \cos^2 a \end{aligned}\]