Final answer:
To solve sin(4x-10) - cos(x+6), we can use trigonometric identities and properties. First, we rewrite sin(4x-10) and cos(x+6) using trigonometric identities. Then, we simplify the equation by combining like terms.
Step-by-step explanation:
To solve the equation sin(4x-10) - cos(x+6), we can use trigonometric identities and properties. First, we can rewrite sin(4x-10) as sin(4x)cos(10) - cos(4x)sin(10). Then, we can rewrite cos(x+6) as cos(x)cos(6) - sin(x)sin(6). Now, we can substitute these values back into the original equation:
sin(4x)cos(10) - cos(4x)sin(10) - (cos(x)cos(6) - sin(x)sin(6))
Next, we can simplify the equation by combining like terms:
sin(4x)cos(10) - cos(4x)sin(10) - cos(x)cos(6) + sin(x)sin(6)
Finally, we have:
sin(4x)cos(10) - cos(x)cos(6) - cos(4x)sin(10) + sin(x)sin(6)
So, the solution to the equation sin(4x-10) - cos(x+6) is sin(4x)cos(10) - cos(x)cos(6) - cos(4x)sin(10) + sin(x)sin(6).