Question

tg6x+tg3x-tg9x=0 решить уравнение немогу решить помогите

Answer 1

tg(α + β) =(tgα + tgβ)/(1 - tgαtgβ)

tg6x + tg3x = tg(6x + 3x)(1 - tg6xtg3x) = tg9x(1 - tg6xtg3x)

tg6x + tg3x - tg9x = 0

tg9x(1 - tg6xtg3x) - tg9x = 0

tg9x(1 - tg6xtg3x - 1) = 0

tg9xtg6xtg3x = 0

tg9x = 0 или tg6xtg3x = 0

9x = πk или 6x = πk или 3x = πk, k∈Z

x = πk/9 или x = πk/6 или x = πk/3