Question

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

Answer 1

$(sin^2a-cos^2a)^2+2cdot cos^2acdot sin^2x=\\=[; (A-B)^2=A^2-2AB+B^2; ]=\\=sin^4a-underline {2cdot sin^2acdot cos^2a}+cos^4a+underline {2cdot cos^2acdot sin^2a}=\\=sin^4a+cos^4a$