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sin4x-cos^4x=-sin^4x

Sin4x=cos⁴x-sin⁴x

sin4x = (cos²x+sin²x) (cos²x-sin²x)

sin4x=1*cos2x

2sin2x*cos2x=cos2x

2sin2x*cos2x-cos2x=0

cos2x (2sin2x-1) = 0

cos2x=0

2x=π/2+πk, k∈Z

x=π/4+πk/2

2sin2x-1=0

sin2x=1/2

2x=π/6+2πk, k∈Z

x=π/12+πk

2x=5π/6+2πk, k∈Z

x=5π/12+πk

Sin (4x) - cos⁴x=-sin⁴x

sin (4x) = cos⁴x-sin⁴x

sin (4x) = (cos²x-sin²x) (cos²x+sin²x)

sin (4x) = cos (2x) * 1

sin (4x) - cos (2x) = 0

2sin (2x) cos (2x) - cos (2x) = 0

cos (2x) (2sin (2x) - 1) = 0

cos (2x) = 0 или 2sin (2x) - 1=0

2x=π/2+πn, n∈Z 2sin (2x) = 1

x₁=π/4+πn/2, n∈Z sin (2x) = 1/2

2x = (-1) ⁿ * π/6+πn, n∈Z

x₂ = (-1) ⁿ * π/12+πn/2, n∈Z