Доказать тождество cos^4a + sin^2a + sin^2a cos^2a = 1

Cos^4 A + sin^2 A + sin^2 A * cos^2 A= (cos^2 A)^2  + sin^2 A * cos^2 A + sin^2 A  = cos^2 A *(cos^2 A + sin^2 A) + sin^2 A = { sin²x+cos²x=1} = cos^2 A * 1 + sin^2 A = 1