Question

Помогите вычислить 10 класс

Answer 1

Решение:

а) 2cos(arccos √2/2) + 4sin(arcsin √2/2) = 2×√2/2 + 4×√2/2 = √2 + 2√2 = 3√2

б) tg²(arctg(-1/√3)) - ctg²(arcctg √3) = (-1/√3)² - (√3)² = (-√3/3) - 3 = 3/9 - 3 = -8/3

в) arcsin(sin π/12) + arccos(cos π/9) - arctg(tg π/3) + arcctg(ctg π/6) = π/12 + π/9 - π/3 + π/6 = 3π/36 + 4π/36 - 12π/36 + 6π/36 = 3π + 4π - 12π + 6π/36 = π/36

г) arccos(sin π/3) - arcsin(cos 0) = arccos √3/2 - arcsin 1 = π/6 - π/2 = π - 3π/6 = - 2π/6 = -π/3