Given,

Let cosx=t

-sinx dx=dt

Now, t²-2t-3

= t²-3t+t-3

= t(t-3)+t-3

= (t-3) (t+1)

1≅ A(t-1)+B(t-3)

Equating ’t’ coeff:-

0=A+B

A=-B

Equating constant:-

1=-A-3B

1=-(-B)-3B

1=-2B