Question

Given 0 ≤ θ < 2π, solve 2 csc x = 3 cscθ -cscθ sinθ

Answer 1

θ = π/2

Explanation:

2 csc θ = 3 csc θ − csc θ sin θ

Cosecant is the inverse of sine, so the last term is 1:

2 csc θ = 3 csc θ − 1

Combine like terms:

1 = csc θ

Take the inverse and flip sides:

sin θ = 1

Solve for θ given the domain:

θ = π/2