Если ctg a=4, то значение tg(pi/4-2а) =?

1. Вычислим чему равен tg (a):tg (a) = 1 / ctg (a) = 1/4;2. Вычисляем tg (π/4 - 2 * а) по формуле tg (a - b) = (tg (a) + tg (b) ) / (1 + tg (a) * tg (b) ):tg (π/4 - 2 * a) = (tg (π/4) - tg (2 * a) / (1 + tg (π/4) * tg (2 * a) = (1 - tg (2 * a) * (1 + tg (2 * a) = (1 - 2 * tg (a) / (1 - tg^2 (a) ) ) / (1 + 2 * tg (a) / (1 - tg^2 (a) ) = ( (1 - (2 / 4) ) / (1 - 1 / 16) ) / (1 + (2 / 4) / 1 - 1 / 16) ) = (1 - 8 / 15) /(1 + 8 / 15) = 7/15 / 23/15 = 7/15 * 15/23 = 7/23.3. Ответ: tg (π/4 - 2 * а) = 7/23.