1) Вычеслите: sin 105 2) Упростите: sin (180-a) + cos (90+a) 3) ctg40*tg140

1) sin 105 = sin (60 - 45) = sin 60 * cos 45 + cos 60 * sin 45 = (√3 / 2) * (1 / √2) + (1 / 2) * (1 / √2) = (√2 / 4) * (√3 + 1) = 1 / 4 * (√6 + √3)

2) sin (180 - a) + cos (90 + a) = sin 180 * cos a - cos 180 * sin a + cos 90 * cos a - sin 90 * sin a = 0 * cos a - ( - 1) * sin a + 0 * cos a - 1 * sin a = sin a - sin a = 0

3) ctg 40 * tg 140 = ctg (180 - 40) * tg 40 = - ctg 40 * tg 40 = 1