2sin x/2 = 1-cosx

Question

Алгебра

Измаил

19 мая, 16:53

2sin x/2 = 1-cosx

+1

Ответы (2)

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Адель · Answer 1

1-cosx=2*sin (x/2)

2sin² (x/2) - 2sin (x/2) = 0

sin (x/2) (sin (x/2) - 1) = 0

a) sin (x/2) = 0

x/2=πn

x1=2πn

б)

sin (x/2) - 1=0

sin (x/2) = 1

x/2=π/2+2πn

x2=πn+4πn

Татьяна · Answer 2

Cos (2*x/2) = 1 - 2sin^2 (x/2)

2sin (x/2) = 1 - 1 + 2sin^2 (x/2)

замена: sin (x/2) = t, t∈[-1; 1]

2t^2 - 2t = 0

2t * (t - 1) = 0

t=0, t=1

sin (x/2) = 0, x/2 = π + 2πk, x = 2π + 4πk

sin (x/2) = 1, x/2 = π/2 + 2πk, x = π + 4πk