Question

найдите tg в квадрате альфа, если cos в квадрате альфа=5/13

Answer 1

$cos^2alpha+sin^2alpha=1middivcos^2alphamedskip\1+mathrm{tg}^2alpha=dfrac{1}{cos^2alpha}medskip\mathrm{tg}^2alpha=dfrac{1}{cos^2alpha}-1medskip\cos^2alpha=dfrac{5}{13}Rightarrowmathrm{tg}^2alpha=dfrac{1}{frac{5}{13}}-1=dfrac{13}{5}-dfrac{5}{5}=dfrac{8}{5}$

Ответ. $mathrm{tg}^2alpha=dfrac{8}{5}$