6)=1 3) tg^2 x+2tgx-3=0...

August 2022 1 9 Report

3 тригонометрических уравнения.
1) sin2x=-√2/2
2) cos(x+pi/6)=1
3) tg^2 x+2tgx-3=0

Answers & Comments

Санечка69

Verified answer

1) sin2x= -√2/2    3) tg²x + 2tgx - 3 = 0
   2x = (-1)ⁿ · (-π/4) + πn, n∈ Z    tgx = y
   x = (-1)ⁿ⁺¹ · π/8 + πn/2, n ∈ Z     y² + 2y - 3 = 0
         D = (-2)² - 4 · 1 · (-3) = 16; √16 = 4
2) cos(x + π/6) = 1       y₁ = (-2 + 4)/2 = 1 y₂ = (-2 - 4)/2 = -3
   x + π/6 = 2πn, n ∈ Z    tgx = 1
   x = -π/6 + 2πn, n ∈ Z     x = π/4 + πn, n ∈ Z
       tgx = -3
   x = -arctg3 +πn, n ∈ Z

Howlx Спасибо

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