Question

Если tgα-ctgα=p то, вычислите tg3α-ctg3α.

Answer 1

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.