Question

tg^4a+ctg^4a , если tga-ctga=m.

Answer 1

$tg^4 \alpha+ctg^4\alpha=(tg^4 \alpha-2+ctg^4\alpha)+2=(tg^2 \alpha-ctg^2\alpha)^2+2=$
$=(tg \alpha-ctg\alpha)^2(tg \alpha+ctg\alpha)^2+2=m^2(tg^2 \alpha+2+ctg^2\alpha)+2=$
$=m^2((tg^2 \alpha-2+ctg^2\alpha)+4)+2=m^2((tg \alpha-ctg\alpha)^2+4)+2=$
$=m^2(m^2+4)+2=m^4+4m^2+2.$