Упростите tg (x+75)- tg (x+15)

Question

Упростите tg (x+75)- tg (x+15)

Answer 1

Решение
tg (x+75) - tg (x+15) = [sin(x + 75 - x - 15)] / [cos(x + 75)*(cos(x + 15)] = 
= sin(60) / [(1/2)* (cos(x + 75 - x - 15) + cos(x + 75 + x + 15))] =
= (√3/2) / [(1/2)*(cos60 + cos(2x + 90)] = √3 / [(1/2) - sin2x) = 
= 2√3 / (1 - 2sin2x)