Задача 66529 ...
Условие
(2 sin²t + 2 cos²t)/(3-sin²t -cos²t) -1/sin²t =-ctg²t
математика 10-11 класс
226
Решение
★
[m]\frac{2sin^2(t) + 2cos^2(t)}{3-sin^2(t) - cos^2(t)} - \frac{1}{sin^2(t)} = -ctg^2(t)[/m]
[m]\frac{2(sin^2(t) + cos^2(t))}{3-(sin^2(t) + cos^2(t))} - \frac{1}{sin^2(t)} = \frac{2*1}{3-1} - \frac{1}{sin^2(t)} = 1-\frac{1}{sin^2(t)} =[/m]
[m]= \frac{sin^2(t) - 1}{sin^2(t)} = \frac{-cos^2(t)}{sin^2(t)} = -ctg^2(t)[/m]
Доказано!