Final answer:
After combining like terms and solving the equation, the cosine value equals 1, which corresponds to an angle of 0° within the given interval. However, this angle is not listed in the provided answer choices, which suggests an error in the question or answer options.
Step-by-step explanation:
To solve the equation −2+6cosx=8−4cosx for 0°≤x≤180°, we first combine like terms:
- Add 4cosx to both sides: −2 + 6cosx + 4cosx = 8
- Combine the cosx terms: 10cosx = 10
- Divide both sides by 10: cosx = 1
Now, we need to find the value of x for which the cosine is equal to 1. Within the given interval, x can only be 0° as cos(0°) = 1. However, since 0° is not an option given in the question, this indicates there has been a typo or a misunderstanding in the question or provided answers since cos(180°) = -1. Therefore, none of the provided options are correct.
It's important to know the basic trigonometric values and to always verify that the calculated result falls within the given interval.