Question

решите уравнение sin2x + 2os^2x= 4sin^2x

Answer 1

sin2x+2cos²x=4sin²x
2sinx*cosx+2cos²x-4sin²x=0 | :cos²≠0
2tgx+2-4tg²x=0 |: (-2)
tg²x-tgx-2=0
tgx=y
y²-y-2=0
y₁=2, y₂=-1
1. tgx=2, x₁=arctg2+πn, n∈Z

2. tgx=-1, x₂=-π/4+πn, n∈Z