Question

Упростить выражение:..

Answer 1

$frac{ sin^{2}x-cos^{2}x+cos^{4}x }{cos^{2}x-sin^{2}x+sin^{4}x}=frac{sin^{2}x-cos^{2}x(1-cos^{2}x)}{cos^{2}x-sin^{2}x(1-sin^{2}x)}=frac{sin^{2}x-cos^{2}xsin^{2}x}{cos^{2}x-sin^{2}xcos^{2}x}=$
$=frac{sin^{2}x(1-cos^{2}x)}{cos^{2}x(1-sin^{2}x)}=frac{sin^{2}xsin^{2}x}{cos^{2}xcos^{2}x}=frac{sin^{4}x}{cos^{4}x}=tg^4x$