Question

ДОКАЗАТЬ ТОЖДЕСТВО
cos^4a + sin^2A + sin^2A cos^2A = 1

Answer 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