High School

Select all the solutions of the given equation for [tex]0^\circ < \theta < 360^\circ[/tex].

[tex]\csc\theta\cos\theta - 2\cos\theta = 0[/tex]

A. 90

B. 270

C. 150

D. 180

E. 30

F. 210

Answer :

Final answer:

The solutions for the given equation for 0∘<θ<360∘ are 90°, 270°, 30°, and 150°

Explanation:

To solve the equation cscθcosθ−2cosθ=0, we can factor out cosθ from the left side:

cosθ(cscθ - 2) = 0

Now we have two possibilities:

  1. cosθ = 0
  2. cscθ - 2 = 0

Let's solve each equation separately:

  1. From cosθ = 0, we can get θ = 90° and θ = 270°
  2. From cscθ - 2 = 0, we can solve for cscθ:

Therefore, the solutions for the given equation for 0∘<θ<360∘ are:

  • θ = 90°
  • θ = 270°
  • θ = 30°
  • θ = 150°

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