Question

tgX+ctgX=5 tg²X+ctg²X=?​

Answer 1

Поскольку $mathop{mathrm{tg}}xmathop{mathrm{ctg}}x=1$, то

$(mathop{mathrm{tg}}x+mathop{mathrm{ctg}}x)^2=mathop{mathrm{tg}}^2x+2mathop{mathrm{tg}}xmathop{mathrm{ctg}}x+mathop{mathrm{ctg}}^2x=mathop{mathrm{tg}}^2x+mathop{mathrm{ctg}}^2x+2$

В данном случае

$mathop{mathrm{tg}}^2x+mathop{mathrm{ctg}}^2x=(mathop{mathrm{tg}}x+mathop{mathrm{ctg}}x)^2-2=25-2=23$