Answer:
Step-by-step explanation:
We can simplify the given equation as follows:
3 cot² θ - 1 = 0
3 cot² θ = 1
cot² θ = 1/3
Taking the square root of both sides, we get:
cot θ = ±1/√3
Using the definition of cotangent, we know that:
cot θ = cos θ / sin θ
So we can rewrite the above equation as:
cos θ / sin θ = ±1/√3
Multiplying both sides by √3 and simplifying, we get:
cos θ = ±sin θ / √3
Squaring both sides and using the identity sin² θ + cos² θ = 1, we get:
1/3 = sin² θ + (sin θ / √3)²
Multiplying both sides by 3, we get:
1 = 3 sin² θ + sin² θ
4 sin² θ = 1
sin θ = ±1/2
Therefore, the possible solutions for θ are:
θ = 30°, 150°, 210°, 330°
Now we can check the given choices to see which one is not a solution to the equation:
- 45°: not a solution, since sin 45° = √2/2 ≠ ±1/2
- 150°: a solution, since sin 150° = -1/2 and cos 150° = -√3/2
- 210°: a solution, since sin 210° = -1/2 and cos 210° = √3/2
- 330°: a solution, since sin 330° = 1/2 and cos 330° = -√3/2
Therefore, the choice that is not a solution to the equation is -45°.