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.
solve for the equation
sin(4x - 10) -cos(x+60)=0
1 answer