Вычислите: sinп/8cosп/8tgп/8ctg9 п/8

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