Question

Выразите ,пожалуйста: cos^4 a - cos^2 a + sin^2 a через sin a

Answer 1

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