1) sin(pi/3 - x) = 1/sin(pi/3)cos(x) - cos(pi/3)sin(x) = 1/(√3/2)cos(x) - (1/2)sin(x) = 1/√3cos(x) - sin(x) = 1
По формуле тригонометрической заменыsin(x) = √(1 - cos²(x))
√3cos(x) - √(1 - cos²(x)) = 3cos²(x) - 1 - 1 + cos²(x) = 4cos²(x) = cos(x) = ±√2/cos(x) = ±1/√x1 = pi/4 + 2pin, x2 = 7pi/4 + 2pin
2) 3tg^2(x) = -√tg^2(x) = -√3/tg(x) = ±√(-√3/3tg(x) = ±i√(√3/3x1 = pi/3 + pin, x2 = 2pi/3 + pin, x3 = 4pi/3 + pin, x4 = 5pi/3 + pin
1) sin(pi/3 - x) = 1/
sin(pi/3)cos(x) - cos(pi/3)sin(x) = 1/
(√3/2)cos(x) - (1/2)sin(x) = 1/
√3cos(x) - sin(x) = 1
По формуле тригонометрической замены
sin(x) = √(1 - cos²(x))
√3cos(x) - √(1 - cos²(x)) =
3cos²(x) - 1 - 1 + cos²(x) =
4cos²(x) =
cos(x) = ±√2/
cos(x) = ±1/√
x1 = pi/4 + 2pin, x2 = 7pi/4 + 2pin
2) 3tg^2(x) = -√
tg^2(x) = -√3/
tg(x) = ±√(-√3/3
tg(x) = ±i√(√3/3
x1 = pi/3 + pin, x2 = 2pi/3 + pin, x3 = 4pi/3 + pin, x4 = 5pi/3 + pin