Final answer:
To find the value of x where sin(4x-10) equals cos(40-x), we use the co-function identity, leading to the solution x=20, making x=20 the correct answer.
Step-by-step explanation:
The question asks us to find the value of x such that sin(4x−10) equals cos(40−x). To solve this, we can make use of the co-function identity which states that sin(90° − θ) = cos(θ).
Therefore, by setting 4x − 10° = 90° − (40° − x), we can find the value of x.
Let's solve the equation:
- 4x − 10° = 50° + x
- 3x = 60°
- x = 20°
Therefore, the correct option answer to the question is x=20.