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We know that -1≤sin x≤1
2sin x=5
sin x=2.5 and it's not true.
So the answer will be ∅
1-sin²(x/2-3π)-cos²(x/4)+sin²(x/4)=(1-sin²(x/2-3π))-(cos²(x/4)-sin²(x/4))=
=cos²(x/2-3π)-cos(2*(x/4))=(cos(3π-x/2))²-cos(x/2)=(-cos(x/2))²-cos(x/2)=cos²(x/2)-cos(x/2)
Cos^2x = 1/2
cosx = - √2/2
x₁ = ± arccos(-√2/2) + 2πn
x₁ = ± (π - π/4) + 2πn
x₁= ± 3π/4 + 2πn, n∈Z
cosx = √2/2
x₂ = ± arccos(√2/2) + 2πk
x₂ = ± π/4 + 2πk, n∈Z