Question

Sin(30x-60)=-sin(10-2x)

Answer 1

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.