Question

Верно ли равенство ?

Answer 1

14)
 а) sin7π/12 -sinπ/12 =2sin(7π/12-π/12)/2*cos(7π/12+π/12)/2=2sinπ/4*cosπ/3 =2*√(2/2)*1/2  =√2/2 .   Да.
б) cos11π/24 -cosπ/8 = -2sin(11π/24 -π/8)/2* sin(11π/24 +π/8)/2  =
 -2sin(11π/24 -π/8)/2* sin(11π/24 +π/8)/2 =-2sinπ/6*sin7π/24 = -2*1/2*sin7π/24 =
=- sin7π/24.   Да.
в) sin11π/18 +sin7π/18 =2sinπ/2*cosπ/9 =2*1*cosπ/9 =2cosπ/9 ≠cos2π/9.   Нет .
г) cos5π/8 + cos5π/8 =2cos(5π/8 - π/8)/2 *cos(5π/8+ π/8)/2 =
2cos(5π/8 - π/8)/2 *cos(5π/8+ π/8)/2 =2cosπ/4*cos3π/8 =2*(√2/2)*cos3π/8=
√2cos3π/8. Да.