Ответ:
Пошаговое объяснение:
1) sin(a + b) = sina * cosb + cosa * sinb
cosa = √(1 - 9/25) = 4/5
cosb = √(1 - 576/625) = 7/25
sin(a + b) = 3/5 * 7/25 + 4/5 * 24/25 = 117/125
3) cos(a + b) = cosa * cosb - sina * sinb
sina = √(1 - 16/25) = 3/5
sinb = √(1 - 144/169) = 5/13
cos(a + b) = 4/5 * 12/13 - 3/5 * 5/13 = 33/65
5) tga = sina/cosa = sina/√(1-sin²a) = 7/24
24sina = 7√(1-sin²a)
576sin²a = 49 - 49sin²a
625sin²a = 49
sin²a = 49/625
sina = 7/25
cosa = √(1-49/625) = 24/25 (>0, т.к. tga > 0)
sin(a + π/4) = √2/2 * (sina + cosa) = √2/2 * (7/25 + 24/25) = 31√2/50