Question

Упростите выражение: sin^4x + sin^2x * cos^2x - 1

Answer 1

Ответ:

$sin^4x+sin^2x\cdot cos^2x-1=\\\\=(sin^4x+2\, sin^2x\cdot cos^2x+cos^4x)-sin^2x\cdot cos^2x-cos^4x-1=\\\\=(\underbrace {sin^2x+cos^2x}_{1})^2-cos^4x-sin^2x\cdot cos^2x-1=\\\\=1-cos^4x-sin^2x\cdot cos^2x-1=-cos^2x\, (\underbrace {cos^2x+sin^2x}_{1})=-cos^2x$