Question

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

Answer 1

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