Question

Вычислите: sinп/8cosп/8tgп/8ctg9п/8

Answer 1

tgα*ctgα=1
sin2α=2sinαcosα⇒sinαcosα=1/2*sin2α⇒
sinπ/8cosπ/8=1/2*sin(2*π/8)=1/2*sinπ/4
ctg9π/8=ctg(π+π/8)=ctgπ/8 - по формулам привидения

sinπ/8cosπ/8*tgπ/8ctg9π/8=1/2*sinπ/4*tgπ/8ctgπ/8=1/2*√2/2*1=√2/4
Ответ: √2/4