Решите уравнение 3ctg 2 x = 2tg 2 x - 5.

3ctg2x = 2tg2x - 5

3 = 2tg2x - 5

tg2x

Пусть tg2x=y

3 = 2y - 5

y

y≠0

y (2y-5) = 3

2y²-5y-3=0

D=25+4*2*3=25+24=49

y₁=5-7 = - 2/4 = - 1/2

4

y₂=5+7=3

4

При у = - 1/2

tg2x = - 1/2

2x=π - arctg1/2 + πn, n∈Z

x=π/2 - 1/2 arctg 1/2 + πn/2, n∈Z

x=π/2 (n+1) - 1/2arctg1/2, n∈Z

При у=3

tg2x=arctg3 + πn, n∈Z

x=1/2 arctg3 + πn/2, n∈Z