Answer :

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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