sin^3(23pi/24)cos(pi/24) + cos^3(23pi/24)sin(pi/24)
sin(23pi/24)cos(23pi/24) = sin(23pi/24)cos(23pi/24) = 1/2(sin(46pi/24))
cos(pi/24) = cos(pi/24) = cos(pi/24) = cos(2pi/48) = cos(pi/48).tg(23pi/48) sin(pi/48) = 1/2(cos(46pi/48))sin(pi/48) + cos(46pi/24) sin(pi/24)sin(pi/48) = 1/2(1/2)sin(2pi/48) + cos(2pi/48) (1/2)sin(pi/48) = 1/4sin(pi/24) + cos(pi/24) 1/2sin(pi/48) = 1/4sin(pi/24) + cos(pi/24) 1/2sin(pi/48) = 1/4(1/2sin(pi/24)cos(pi/48)) + cos(2pi/48) 1/2(1/2sin(pi/24)) = 1/4(1/2(1/2sin(pi/24)cos(pi/48))) + 1/2(1/2sin(pi/24)cos(pi/48)) = 1/8(1/2sin(pi/24)cos(pi/48)) + 1/2(1/2sin(pi/24)cos(pi/48)) = 1/8(1/2sin(pi/24)cos(pi/48)) + 1/2(1/2sin(pi/24)cos(pi/48)) = 1/8(1/2sin(pi/24)cos(pi/48)) + 1/8(1/2sin(pi/24)cos(pi/48)) = 1/4sin(pi/24)cos(pi/48) + 1/4sin(pi/24)cos(pi/48) = 1/4(sin(pi/24)cos(pi/48) + sin(pi/24)cos(pi/48)) = 1/4(sin(pi/24)cos(pi/48)) + 1/4sin(pi/24)cos(pi/48).Если sina=(-0.8) и a принадлежит промежутку (270º;360º), то значение tg(a-(3pi/4)) равно:
sin(a) = -0.8
cos(a) = -√(1-sin^2(a)) = -√(1-(-0.8)^2) = -√(1-0.64) = -√0.36 = -0.6
tg(a) = sin(a)/cos(a) = -0.8/(-0.6) = 4/3.
a-(3pi/4) = atan(tg(a)) - 3pi/4 = atan(4/3) - 3pi/4 ≈ 63.43° - 3pi/4 = 315° - 270° = 45°
tg(a-(3pi/4)) = tg(45°) = 1.