Решить уравнение:
2tgx+2ctgx=5
2tgx + 2ctgx = 5
2tgx + 2/tgx - 5 = 0
2tg²x - 5tgx + 2 = 0
замена: tgx = a
2a² - 5a + 2 = 0
a₁ = 2, a₂ = 1/2
обратная замена:
tgx = 2
x = arctg2 + πn, n∈Z
tgx = 1/2
x = arctg(1/2) + πn, n∈Z
ctg x=1/tg x, tgx=t:
2t+2/t=5
2t^2-5t+2=0
D=25-4*2*2=9
t=(5+-3)/4
t=2 or t=1/2
tgx=2 or tgx=1/2
x=arctg2+pi*k, k in Integers OR x=arctg0.5 + pi*m, m in Integers