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,