Answer:
To find the value of x that satisfies the equation cos(50 + x) = sin(2x - 6), we will need to solve for x. Let's go step by step:
1. We can start by rearranging the equation to isolate one of the trigonometric functions. In this case, let's isolate sin(2x - 6):
sin(2x - 6) = cos(90 - (2x - 6))
2. The sum-to-product identity states that sin(A) = cos(90 - A). Applying this identity to our equation, we have:
sin(2x - 6) = sin(90 - (2x - 6))
3. Now, we can set the arguments inside the trigonometric functions equal to each other:
2x - 6 = 90 - (2x - 6)
4. Simplifying the equation, we get:
2x - 6 = 90 - 2x + 6
4x = 90
5. To solve for x, we divide both sides of the equation by 4:
x = 90 / 4
x = 22.5
Therefore, the value of x that satisfies the given equation is approximately 22.5 to the nearest tenth.