Question

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

Answer 1

Помним, что

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

Решение

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

Answer 2

sin² a + sin² a ∗ cos² a + cos⁴ a=(sin² a)*(1+cos²a)+ cos⁴ a=

(sin² a)*(sin² a+cos²a+cos²a)+ cos⁴ a=sin⁴ a+2sin²a*cos²a+cos⁴ a=

(sin² a+cos²a)²=1