Arctg(tg7π/8) = arctg[tg(π-π/8)]= arctg(-tgπ/8)= -arctg(tgπ/8) = -π/8
cos[arccos(-1/2)+π/3]= cos(arccos(-1/2)·cosπ/3 - sin(arccos(-1/2)·sinπ/3=
= cos(π-arccos1/2) · 1/2 - sin(π-arccos1/2) · √3/2 =
= - cos(arccos1/2) ·1/2 - √3/2 · sin(arccos1/2) =
= -1/2 ·1/2 - √3/2 · √(1-cos²(arccos1/2)) = - 1/4 - √3/2 ·√(1 - (1/2)²) =
= - 1/4 - √3/2 · √3/2 = -1/4 - 3/4 = - 1
4/π · (-π/8) + tg2x = 1/2 ·(-1)
- 1/2 + tg2x = - 1/2
tg2x = 0
2x = πk
x = π/2 ·k k∈N