Question

Помогите, пожалуйста, с заданием:))) Вычислите sin t+cos t, если tg t - 1/tg t=-7/12 и 0<t</2

Answer 1

$\frac{tgt-1}{tgt}=-\frac{7}{12}\\ 1-\frac{1}{tgt}=1-ctgt=-\frac{7}{12}\\ ctgt=\frac{19}{12}\\ \frac{cost}{sint}=\frac{19}{12}\\ \frac{cost}{\sqrt{1-cos^2t}}=\frac{19}{12}\\ \frac{cos^2t}{1-cos^2t}=\frac{361}{144}\\ 144cos^2t=361-361cos^2t\\ cost = \sqrt{\frac{361}{505}}=\frac{19}{\sqrt{505}}\\ sint=\sqrt{\frac{505-361}{505}} = \frac{12}{\sqrt{505}}\\ cost+sint=\frac{31}{\sqrt{505}}$