Evaluate:

Let

Putting t=cos x

dt=-sin x dx

Now putting,

A(t-2)+B(t+1)=-t

Now put t-2=0

Therefore, t=2

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

Now put t+1=0

Therefore, t=-1

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

Now From equation (1) we get,

So,