Question

For any θ ∈ (π/4, π/2), the expression 3(sinθ - cosθ)⁴ + 6 (sinθ + cosθ)² + 4sin⁶θ equals: (A) 13 - 4cos²θ + 6sin²θ cos²θ (B) 13 - 4cos⁶θ
(C) 13 - 4cos²θ + 6cos⁴θ (D) 13 - 4cos⁴θ + 2sin²θ cos²θ
[JEE Main 2019]

Answer 1

Option no. A is true

Answer 2

$\huge\star\underline\mathfrak\red{Answer:-}$

For any θ ∈ (π/4, π/2), the expression 3(sinθ - cosθ)⁴ + 6 (sinθ + cosθ)² + 4sin⁶θ equals:

(A) 13 - 4cos²θ + 6sin²θ cos²θ ✔✔✔

(B) 13 - 4cos⁶θ

(C) 13 - 4cos²θ + 6cos⁴θ

(D) 13 - 4cos⁴θ + 2sin²θ cos²θ