Ctg5pi/8+ctg9pi/8 ПОМОГИТЕ ПОБЫСТРЕЕ ПЛИИИЗ

Question

Ctg5pi/8+ctg9pi/8 ПОМОГИТЕ ПОБЫСТРЕЕ ПЛИИИЗ

Answer 1

Ctg 5π/8 - tg 5π/8 = Сos5π/8/Sin5π/8 - Sin5π/8/Cos5π/8 = 
= (Cos² 5π/8 - Sin²5π/8)/Sin 5π/8 ·Cos 5π/8= Cos 10π/8/1/2Sin10π/8 =
= 2Сtg 10π/8 =2 Сtg 5π/4 = - 2