tgα-ctgα=p
tg³α-ctg³α=(tgα-ctgα)*(tg²α+tgα*ctgα+ctg²α)=
=p*(tg²α-2*tgα*ctg²α+ctg²α+3*tgα*ctgα)=p*(tgα-ctgα)²+3*1=p*p²+3=p³+3.
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tgα-ctgα=p
tg³α-ctg³α=(tgα-ctgα)*(tg²α+tgα*ctgα+ctg²α)=
=p*(tg²α-2*tgα*ctg²α+ctg²α+3*tgα*ctgα)=p*(tgα-ctgα)²+3*1=p*p²+3=p³+3.