Tg(pi x)cos(2x-pi/2)=cos(-pi/3) решить,

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