3 тригонометрических уравнения.
1) sin2x=-√2/2
2) cos(x+pi/6)=1
3) tg^2 x+2tgx-3=0
1) sin2x=-√2/2
2) cos(x+pi/6)=1
3) tg^2 x+2tgx-3=0
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1) sin2x= -√2/2 3) tg²x + 2tgx - 3 = 02x = (-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