Question

Упростить: 1-2sin^2(a)+sin^4(a)/1-2cos^2(a)+cos^4(a)

Answer 1

$displaystylettboxed{cos^2alpha+sin^2alpha=1}\\ frac{1-2sin^2alpha+sin^4alpha}{1-2cos^2alpha+cos^4alpha}=frac{(1-sin^2alpha)^2}{(1-cos^2alpha)^2}=(frac{cos^2alpha}{sin^2alpha})^2=(ctg^2alpha)^2=ctg^4alpha$