Question

Let A_n be the area bounded by the curve y = (1 + tanx)ⁿ and the lines x = 0, y = 0, and x = π/4. Prove that for n ≥ 2, A_n + A_{n - 2} = 1/(n - 1)  and deduce 1/(2n + 2) < A_n < 1/(2n - 2).

Answer 1

(1 + tanx)ⁿ > (tanx)ⁿ so, we can replace