Tg(x+75) - tg(x+15) упростить

Question

Tg(x+75) - tg(x+15) упростить

Answer 1

Решение
tg(x+75) - tg(x+15) = [sin(x + 75 - x - 15)]/[cos75cos15] =
 = sin60/[cos(90 - 15)*cos15)] = (√3/2) / [sin15*cos15] = 
 (√3) / [2*sin15*cos15] = √3 / sin30 = √3/(1/2) = 2√3