sec²(x4)−1cos(6x)−cos(2x) =(sec²(x4)−1)⋅1cos(6x)−cos(2x) =sin2(4x)Cos2(4x)⋅1cos(4x+2x)−cos(2x)
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cos(4x+2x)−cos(2x) =cos(2x)cos(4x)−sin(2x)sin(4x)−cos(2x) =cos(2x)[cos2(2x)−sin2(2x)]−sin(2x)[2sin(2x)cos(2x)]−cos(x2) =cos(2x){cos2(2x)−sin2(2x)−2sin2(2x)−1} =cos(2x){−sin2(2x)−sin2(2x)−2sin2(2x)} =cos(2x){−4sin2(2x)} =−4cos(2x)sin2(2x)
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sin2(4x)Cos2(4x) =(sin(4x))2(Cos(4x))2 =(2sin(2x)cos(2x))2(Cos2(2x)−sin2(2x))2 =4sin2(2x)cos2(2x)Cos2(4x)
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=4sin2(2x)cos2(2x)Cos2(4x)⋅1−4cos(2x)sin2(2x) =−cos(2x)Cos2(4x) =−cos(2x)Sec2(4x)
=−cos(2x)Sec2(4x)
. Please help
sec2(4x)−1cos(6x)−cos(2x)
sec2(4x)−1cos(6x)−cos(2x)sec2(4x)−1=sin2(4x)cos2(4x) =sin2(4x)sec2(4x)=sin2(4x)sec2(4x)cos(6x)−cos(2x)cos(6x)−cos(2x)=−2sin(6+2x2)sin(6−2x2) =−2sin(4x)sin(2x)=sin2(4x)sec2(4x)−2sin(4x)sin(2x)=−sin(4x)sec2(4x)2sin(2x)=−sin(2⋅2x)sec2(4x)2sin(2x)sin(2⋅2x)=2sin(2x)cos(2x)=−2sin(2x)cos(2x)sec2(4x)2sin(2x)=−cos(2x)sec2(4x)