Найдите значение выражения
ctg п/8 * tg п/8 + 1

ответ:

tg(3π/8)·tg(π/8)=(sin(3π/8)·sin(π/8))/(cos(3π/8)·cos(π/8))=

=(1/2)(cos(2π/8)–cos(4π/8))/(1/2)(cos(4π/8)+cos(2π/8))

так как cos(4π/8)=cos(π/2)=0,

cos(2π/8)=cos(π/4), то

tg(3π/8)·tg(π/8)+1=

=cos(π/4)/cos(π/4)+1=2

о т в е т. 2

пошаговое объяснение:

tg(3π/8)·tg(π/8)=(sin(3π/8)·sin(π/8))/(cos(3π/8)·cos(π/8))=

=(1/2)(cos(2π/8)–cos(4π/8))/(1/2)(cos(4π/8)+cos(2π/8))

так как cos(4π/8)=cos(π/2)=0,

cos(2π/8)=cos(π/4), то

tg(3π/8)·tg(π/8)+1=

=cos(π/4)/cos(π/4)+1=2

о т в е т. 2