x = ± π/6 + πn (n∈Z)
Объяснение:
Исправим условие: tg (pi + x) · cos (2x - π/2) = cos (-π/3)
tg x · sin2x = 1/2
(sinx/cosx )· 2sinx · cosx = 1/2
cos x ≠ 0
2sin²x = 1/2
2 · (1 - cos2x)/2 = 1/2
1 - cos 2x = 1/2
cos 2x = 1/2
2x = ± π/3 + 2πn
x = ± π/6 + πn
x = ± π/6 + πn (n∈Z)
Объяснение:
Исправим условие: tg (pi + x) · cos (2x - π/2) = cos (-π/3)
tg x · sin2x = 1/2
(sinx/cosx )· 2sinx · cosx = 1/2
cos x ≠ 0
2sin²x = 1/2
2 · (1 - cos2x)/2 = 1/2
1 - cos 2x = 1/2
cos 2x = 1/2
2x = ± π/3 + 2πn
x = ± π/6 + πn