Agar tg\,α+ctg\,α=3 boʻlsa, tg^2α-2tg\,α+ctg\,α ifodaning qiymatini toping.

$\mathrm{tg}\,\alpha+\mathrm{ctg}\,\alpha=3$ ni $\mathrm{tg}\,\alpha=3-\mathrm{ctg}\,\alpha$ ko‘rinishida, $\mathrm{tg}^2\alpha-2\mathrm{tg}\,\alpha+\mathrm{ctg}\,\alpha$ ni esa $\mathrm{tg}\,\alpha(\mathrm{tg}\,\alpha-2)+\mathrm{ctg}\,\alpha$ ko‘rinishida ifodalab olamiz. $\mathrm{tg}\,\alpha(\mathrm{tg}\,\alpha-2)+\mathrm{ctg}\,\alpha$ ifodaning qavs ichidagi $\mathrm{tg}\,\alpha$ ni $3-\mathrm{ctg}\,\alpha$ bilan almashtirib, so‘ng soddalashtiramiz. $\mathrm{tg}\,\alpha(\mathrm{tg}\,\alpha-2)+\mathrm{ctg}\,\alpha=\mathrm{tg}\,\alpha(3-\mathrm{ctg}\,\alpha-2)+\mathrm{ctg}\,\alpha=\mathrm{tg}\,\alpha(1-\mathrm{ctg}\,\alpha)+\mathrm{ctg}\,\alpha=\mathrm{tg}\,\alpha-1+\mathrm{ctg}\,\alpha=\mathrm{tg}\,\alpha+\mathrm{ctg}\,\alpha-1.$ $\mathrm{tg}\,\alpha+\mathrm{ctg}\,\alpha=3$ ekanligini e’tiborga olsak, ifodaning qiymati 2 ga teng bo‘ladi.

Manba: UZBMB namunaviy test topshiriqlari va ularni yechish bo‘yicha tavsiyalar (2020). Sh.A.Alimov va boshqalar. Algebra, umumiy o‘rta ta’lim maktablarining 9-sinfi uchun darslik. “O‘qituvchi” NMIU, Toshkent – 2019