1)cos(π/5)cos(2π/5)=
2)sin10ºsin30ºsin50ºsin70ºsin90º=
3)cos(π/7)cos(4π/7)cos(5π/7)=

1) cos pi/5 * cos 2pi/5 = (4 * sin pi/5 * cos pi/5 * cos 2pi/5)/(4 * sin pi/5) =
= (2 * sin 2pi/5 * cos 2pi/5)/(4 * sin pi/5) = sin 4pi/5 / (4 * sin (pi - 4pi/5)) =
= sin 4pi/5 / (4 * sin 4pi/5) = 1/4.
2) sin 10 * sin 30 * sin 50 * sin 70 * sin 90 = sin 10 * 1/2 * sin 50 * sin 70 * 1 =
= 1/2 * sin 10 * sin 50 * sin 70.
Дальше используем формулу sin a = cos (90 - a).
Тогда
1/2 * sin 10 * sin 50 * sin 70 = 1/2 * cos 20 * cos 40 * cos 80 =
= (1/2 * 8 * sin 20 * cos 20 * cos 40 * cos 80)/(8 * sin 20) = 1/2 * sin 160/(8 * sin 20) =
= 1/16
3) cos pi/7 * cos 4pi/7 * cos 5pi/7 = cos pi/7 * cos 4pi/7 * cos (pi - 2pi/7) =
= -cos pi/7 * cos 2pi/7 * cos 4pi/7 =
= (-8 * sin pi/7 * cos pi/7 * cos 2pi/7 * cos 4pi/7)/(8 * sin pi/7) =
= -sin 8pi/7 / (8 * sin pi/7) = -1/8 * sin (pi + pi/7)/sin pi/7 = 1/8.

спасибо)))