Yes, the expression Asin(x) + Bcos(x) can be further simplified by combining the sine and cosine terms into a single trigonometric function.
To simplify the expression, we can make use of the trigonometric identity:
sin(x - θ) = sin(x)*cos(θ) - cos(x)*sin(θ)
Comparing this identity to the given expression, we can rewrite it as:
Asin(x) + Bcos(x) = R*sin(x - θ)
Where R represents the combined amplitude, and θ represents the phase shift.
To determine the values of R and θ, we can use the following formulas:
R = sqrt(A^2 + B^2) θ = arctan(-B/A)
By substituting these values back into the simplified expression, we have:
Asin(x) + Bcos(x) = sqrt(A^2 + B^2) * sin(x - arctan(-B/A))
This simplified form allows us to express the given expression in terms of a single sine function with a combined amplitude and phase shift.