let

Put t=sinx

dt=cosxdx

Putting

A(1+t)(5-4t)+B(1-t)(5-4t)+C(1+t)(1-t)=1

Now Putting 1+t=0

t=-1

A(0)+B(2)(9)+C(0)=1

Now Putting 1-t=0

t=1

A(2) +B(0)+C(0)=1

Now Putting 5-4t=0

From equation(1),we get,