solve for the equation

sin(4x - 10) -cos(x+60)=0

1 answer

To solve for the equation sin(4x - 10) - cos(x + 60) = 0, we'll first gather like terms.

sin(4x - 10) = cos(x + 60)

Next, we'll use the identity sin(θ) = cos(90 - θ) to rewrite the equation as:

cos(90 - (4x - 10)) = cos(x + 60)

cos(90 - 4x + 10) = cos(x + 60)

cos(100 - 4x) = cos(x + 60)

Since the cosine function is an even function, we have:

cos(x + 60) = cos(100 - 4x)

x + 60 = 100 - 4x

Now, let's solve for x.

5x = 40

x = 8

Therefore, the solution to the equation sin(4x - 10) - cos(x + 60) = 0 is x = 8.