Вопрос пользователя:
1. ctg 15 градусов – tg 15 Градусов=….?
2. cos^4(5pi/12) – sin^4(5pi/12)=…??
Илюха отвечает:
1. ctg 15 – tg 15 = cos15/sin15 – sin15/cos15 = (cos^2 15 – sin^2 15)/(sin15 * cos15) = cos30/sin15*cos15 = sqrt(3)/(2sin15 * cos15) = sqrt(3)/ sin30 = sqrt(3)/ 1/2 = 2sqrt(3)
2. cos^4(5pi/12) – sin^4(5pi/12)= (cos^2 (5pi/12) – sin^2 (5pi/12))(cos^2(5pi/12) + sin^2(5pi/12)) = (cos (5pi/6))*1 = -sqrt(3)/2