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let dx = dx

Put t=sinx

dt=cosxdx

Putting

A(1+t)² +B(1-t)(1+t)+C(1+t)=t

Now Putting 1-t=0

t=1

A(0)+B(0)+C(1+1)=1

Now Putting 1+t=0

t=-1

A(2)² +B(0)+C(0)=-1

By equating the coefficient of t²,we get,A-B=0

From equation(1),we get,