Question

Let A_n be the area bounded by y = tanⁿx, x = 0, y = 0 and x = π/4. Prove that for n ≥ 2.

(i) A_n + A_{n - 2} = 1/(n - 1)

(ii) 1/2_{(n + 1)} < A_n < 1/2_{(n - 1)}

Answer 1

(i) See Fig.

Obviously