Вычислите tg 15°*ctg 75°

Tg15*ctg75=tg15*ctg (90-15) = tg15*tg15=tg²15=sin²15/cos²15 = (1-cos30) / (1+cos30) =

= (1-√3/2) / (1+√3/2) = (2-√3) / (2+√3) = (2-√3) ² / (4-1) = 2-4√3+3=7-4√3

sin²15 = (1-cos30) / 2

cos²15 = (1+cos30) / 2