let 
= 
Put t=cosx
dt=-sinxdx
Putting 
A(1+t)(1+2t)+B(1-t)(1+2t)+C(1-t2)=1
Putting 1+t=0
t=-1
A(0)+B(2)(1-2)+C(0)=1
Putting 1-t=0
t=1
A(2)(3)+B(0)+C(0)=1
Putting 1+2t=0
From equation(1),we get,
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