Tg^4a+ctg^4a , если tga-ctga=m.

[latex]tg^4 alpha+ctg^4alpha=(tg^4 alpha-2+ctg^4alpha)+2=(tg^2 alpha-ctg^2alpha)^2+2= [/latex][latex]=(tg alpha-ctgalpha)^2(tg alpha+ctgalpha)^2+2=m^2(tg^2 alpha+2+ctg^2alpha)+2=[/latex][latex]=m^2((tg^2 alpha-2+ctg^2alpha)+4)+2=m^2((tg alpha-ctgalpha)^2+4)+2=[/latex][latex]=m^2(m^2+4)+2=m^4+4m^2+2.[/latex]