let 
Put t=cos2x
dt=-2sin2xdx
Putting 
A(1-t)+B(t-2)=1
Putting 1-t=0
t=1
A(0)+B(1-2) =1
B=-1
Putting t-2=0
t=2
A(1-2)+B(0) =1
A=-1
From equation (1), we get,
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