Спростити вираз sin^2 a + sin^2 a ∗ cos^2 a + cos^4 a

Помним, что

$sin^2\alpha+cos^2\alpha=1$

Решение

$sin^2\alpha+sin^2\alpha*cos^2\alpha+cos^4\alpha= \\=sin^2\alpha+(sin^2\alpha+cos^2\alpha)*cos^2\alpha=\\=sin^2\alpha+cos^2\alpha = 1\\\\\\--------------------------------\\\sin^2\alpha * cos^2\alpha+cos^4\alpha=sin^2\alpha * cos^2\alpha+cos^2\alpha*cos^2\alpha=(sin^2\alpha+cos^2\alpha)*cos^2\alpha\\$