Sin11п/18+sin7п/18=cos 2п/9 и второе cos 5п/8+cos - вопрос №4402838111871829588238 от serartem73 23.03.2021 03:21

Question

Алгебра: Sin11п/18+sin7п/18=cos 2п/9 и второе cos 5п/8+cos п/8=√2cos 3п/8

serartem73 · Answer

Sin11π/18 +sin7π/18 =2 sin (11π/18+7π/18)/2 *cos(11π/18-7π/18)/2 =
2 sin π/2 *cosπ/9 =2*1*cosπ/9 = 2cosπ/9.

cos5π/8 +cosπ/8 =2cos(5π/8 +π/8)/2*cos(5π/8-π/8)/2 =2cos3π/16*cosπ/4 =
2cos3π/8*(√2)/2 =√2cos3π/16.