Final answer:
The expression sin(xπ/6) can be rewritten using the angle sum formula as sin(x)cos(π/6) + cos(x)sin(π/6). Substituting in the known values of sin(π/6) and cos(π/6), we find the expression doesn't exactly match any of the provided options. The closest one is √3/2 cosx, but it only accounts for part of the sum.
Step-by-step explanation:
The expression σ(xπ/6) can be rewritten using the angle sum formula sin (α ± β) = sin α cos β ± cos α sin β. In this case, xπ/6 can be thought of as x plus π/6. Therefore, we can express sin(xπ/6) as sin(x + π/6) which equals sinx • cos(π/6) + cosx • sin(π/6). We know that cos(π/6) = √3/2 and sin(π/6) = 1/2, therefore,
sin(xπ/6) = sinx • (√3/2) + cosx • (1/2)
Based on the provided options, none exactly match this form. However, if we must choose from the options, the closest one would be option B √3/2 cosx, but it is missing the sinx component, so it is not entirely correct. Therefore, if we strictly follow the expressions provided as options, option B would be the closest, but still incomplete.