What values for θ
(0≤θ≤2θ)
satisfy the equation?
cosθ−tanθcosθ=0
To solve for θ, we can first factor out a cosθ from the equation:
cosθ(1 - tanθ) = 0
Now we have two possibilities for the equation to be true:
1) cosθ = 0
2) 1 - tanθ = 0
For the first possibility, when cosθ = 0, it means that θ = π/2 (90 degrees) or 3π/2 (270 degrees) within the given interval (0≤θ≤2π).
For the second possibility, when 1 - tanθ = 0, we have:
tanθ = 1
This happens when θ = π/4 (45 degrees) within the given interval.
Therefore, the values for θ that satisfy the equation cosθ - tanθcosθ = 0 are θ = π/4, π/2, and 3π/2.