Verified answer

Ответ: Правильный ответ

Объяснение:

[tex]\displaystyle\bf\\\frac{1+tg10^\circ tg55^\circ}{tg55^\circ-tg10^\circ} =\frac{1+\dfrac{1}{Ctg10^\circ} \cdot \dfrac{1}{Ctg55^\circ} }{\dfrac{1}{Ctg55^\circ} -\dfrac{1}{Ctg10^\circ} } =\frac{\dfrac{Ctg10^\circ Ctg55^\circ+1}{Ctg10^\circ Ctg55^\circ} }{\dfrac{Ctg10^\circ-Ctg55^\circ}{Ctg10^\circ Ctg55^\circ} } =\\\\\\=\frac{(Ctg10^\circ Ctg55^\circ+1)\cdot Ctg10^\circ \cdot Ctg55^\circ}{(Ctg10^\circ-Ctg5\circ)\cdot Ctg10^\circ\cdot Ctg55^\circ}=\frac{Ctg10^\circ Ctg55^\circ+1}{Ctg10^\circ-Ctg55\circ}=[/tex]

[tex]\displaystyle\bf\\=Ctg\Big(55^\circ-10^\circ\Big)=Ctg45^\circ=1\\\\Otvet \ : \ 1[/tex]