Answer:
x = 1.79 and x = 2.19.
Explanation:
To solve the equation sin(30x - 60) = -sin(10 - 2x), we can start by using the identity sin(-θ) = -sin(θ):
sin(30x - 60) = sin(2x - 10)
Now, we have two cases to consider:
Case 1: 30x - 60 = 2x - 10
Solving for x in this case:
30x - 2x = 60 - 10
28x = 50
x = 50 / 28
x ≈ 1.79
Case 2: 30x - 60 = -(2x - 10)
Solving for x in this case:
30x - 60 = -2x + 10
30x + 2x = 60 + 10
32x = 70
x = 70 / 32
x ≈ 2.19
Therefore, the two possible values of x in the equation sin(30x - 60) = -sin(10 - 2x) are approximately x = 1.79 and x = 2.19.