Find:

Let sinθ = t

∴ cosθ dθ = dt

put t² = y

∴ 1 = A(4y+1) + B(y+4) = (4A+B)y + (A+4B)

Comparing coefficients of y on both sides-

4A+B = 0 ...(1)

Also compare constant terms-

A+4B = 1 ...(2)

On solving (1) & (2), we get-

A = -(1/15) & B = (4/15)

put t = sinθ