8 sin θ − 4 csc θ = 0

Question

explain how to solve step by step?

Answer 1

The trigonometric equation is 8sinθ - 4cscθ = 0

The reciprocal identity of cscθ is sinθ.

8sinθ - 4(1/sinθ) = 0

(8sin²θ - 4)/sinθ = 0

8sin²θ - 4 = 0(sinθ)

8sin²θ - 4 = 0

8sin²θ =  4

sin²θ =  4/8

sin²θ = 1/2

sin²θ = [1/√2]²

sin²θ = [sin(π/4)]²

sin²θ = sin²(π/4)

The genaral solution of sin²(θ) = sin²(α) is θ = nπ ± α, where n is an integer. 

Solutions are θ = nπ ± π/4.