Question

Let x = ∑(-1)ⁿ(tanθ)²ⁿ, n ∈ [n = 0, ∞] and y = ∑(-1)ⁿ(cosθ)²ⁿ, n ∈ [n = 0, ∞] where θ ∈ (0, π/4), then

(1) x (y + 1) = 1

(2) y (1 – x) = 1

(3) y (x – 1) = 1

(4) y (1 + x) = 1

Answer 1

Answer is (2)

y = 1 + cos2θ + cos4θ + .......