Упрости выражение,сделайте

Question

Алгебра: Упрости выражение,сделайте

я001 · Accepted Answer

1) sinx - (1 - sin^2(x)) - sin^2(x) = 0
sinx - 1 + sin^2(x) - sin^2(x) = 0
sinx = 1
x = 2πk, k∈Z
2) sinx = t ∈[-1;1]
6t^2 + t - 1 = 0, D=1+4*6 = 25
t1 = (-1-5)/12 = -6/12 = -1/2, sinx = -0.5, x = π/6 + 2πk и x = 5π/6 + 2πk, k∈Z
t2 = (-1+5)/12 = 4/12 = 1/3, sinx = 1/3, x = arcsin(1/3) + 2πk и x = π - arcsin(1/3) + 2πk, k∈Z
3) 1 - sin^2(x) - 4sinx + 3 = 0
-sin^2(x) - 4sinx + 4 = 0
sin^2(x) + 4sinx - 4 = 0
sinx = t ∈[-1;1]
t^2 + 4t - 4 = 0, D=16+16=32
t1 = (-4-√32)/2 < -1
t2 = (-4+√32)/2, x = arcsin((-4+√32)/2) + 2πk и x = π - arcsin((-4+√32)/2) + 2πk
4) sinx*(√3*sinx - 3cosx) = 0
sinx = 0, x = πk
tgx = √3, x = π/3 + πk
5) 2sin^2(x) - √3*2sinx*cosx = 0
2sinx*(sinx - √3*cosx) = 0
sinx = 0, x = πk
tgx = √3, x = π/3 + πk

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