а) sin(157π/4) - cos(-28π/3) + ctg(79π/5)sin(157π/4) = sin(39π + π/4) = sin(π/4) = √2/2cos(-28π/3) = cos(-9π + 2π/3) = cos(2π/3) = -1/2ctg(79π/5) = 1/tan(79π/5) = 1/cot(π/5) = tan(π/5) = 1
Подставляем значения:√2/2 + 1/2 + 1 = √2 + 1
б) cos(7π/4) + sin(5π/3) * tg(7π/6)cos(7π/4) = cos(π/4) = √2/2sin(5π/3) = sin(π + 2π/3) = sin(2π/3) = √3/2tg(7π/6) = tan(π/6) = √3/3
Подставляем значения:√2/2 + √3/2 * √3/3 = √2/2 + √3/2 = (√2 + √3) / 2
а) sin(157π/4) - cos(-28π/3) + ctg(79π/5)
sin(157π/4) = sin(39π + π/4) = sin(π/4) = √2/2
cos(-28π/3) = cos(-9π + 2π/3) = cos(2π/3) = -1/2
ctg(79π/5) = 1/tan(79π/5) = 1/cot(π/5) = tan(π/5) = 1
Подставляем значения:
√2/2 + 1/2 + 1 = √2 + 1
б) cos(7π/4) + sin(5π/3) * tg(7π/6)
cos(7π/4) = cos(π/4) = √2/2
sin(5π/3) = sin(π + 2π/3) = sin(2π/3) = √3/2
tg(7π/6) = tan(π/6) = √3/3
Подставляем значения:
√2/2 + √3/2 * √3/3 = √2/2 + √3/2 = (√2 + √3) / 2