Question

докажите тождество cos^2 a - cos^4 a + sin^4 a = sin^2 a

Answer 1

cos^2 a - cos^4 a + sin^4 a = cos^2 a  + sin^4 a - cos^4 a =  cos^2 a + (sin^2 a -  cos^2 a)(sin^2 a +  cos^2 a) = cos^2 a + (sin^2 a -  cos^2 a)*1 = cos^2 a + sin^2 a -  cos^2 a = sin^2 a