Answer:
θ = 45° and θ = 225°.
Step-by-step explanation:
cos(θ) − tan(θ)cos(θ) = 0.
Solving for θ:
Since tan(θ) = sin(θ)/cos(θ), therefore:
cos(θ) - cos(θ)*sin(θ)/cos(θ) = 0.
cos(θ) and cos(θ) cancel out so:
cos(θ) - sin(θ) = 0.
cos(θ) = sin(θ).
sin(θ)/cos(θ) = 1
tan(θ) = 1.
Replace θ by the basic angle c.
tan(c) = 1.
c = tan⁻¹(1).
c = 45° (or π/4 radians).
We know that tangent ratio is positive in the first quadrant and the third quadrant. Therefore:
θ = 0° + c° and θ = 180° + c°
θ = 0° + 45° and θ = 180° + 45°
θ = 45° and θ = 225°
In the range [0°, 360°], there lie two answers!!!
