Question

докажите тождество sin^4a + cos^4a -1= -2 sin^2a cos^2a

Answer 1

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