Решить 1. sin2x=√2 cosx 2. sin2x+√2sinx=0 - вопрос №1222220206261 от kostya196 27.09.2022 07:36

Question

Алгебра: Решить 1. sin2x=√2 cosx 2. sin2x+√2sinx=0

kostya196 · Answer

1) SIn2x = 2SinxCosx

Sin2x = √2Cosx

2SinxCosx - √2Cosx = 0

Cosx(2Sinx - √2) = 0

Cos x = 0 или Sinx = √2/2

x₁ = π/2 + πk, k∈Z

$x_2 = (-1)^k \frac{\pi}{4}+\pi k$

2) 2SinxCosx + √2Sinx = 0

Sinx(2Cosx + √2) = 0

Sinx = 0 или Cosx = -√2/2

x₁ = πk

x₂ = ±3π/4 + 2πk