Question

If θ₁ and θ₂ be respectively the smallest and the largest values of θ in (0, 2π) - {π} which satisfy the equation, 2cot²θ - (5/sinθ) + 4 = 0, then ∫cos²3θdθ, θ ∈ [θ₁, θ₂] is equal to:

(1) 2π/3

(2) π/3 + 1/6

(3) π/9

(4) π/3

Answer 1

Answer is (4)

Answer 2

Answer is (4)

2cos²θ – 5sinθ + 4sin²θ = 0

3sin²θ – 5sinθ + 2 = 0