Question

Sin(84°-a)cos(a+24°)-cos(84°-a)sin(a+24)​

Answer 1

Sin(84⁰ - α)Cos(α + 24⁰) - Cos(84⁰ - α)Sin(α + 24⁰) = Sin(84⁰ - α - α - 24⁰) =

= Sin(60⁰ - 2α)

Answer 2

To simplify the expression $\sin(84°-a)\cos(a+24°)-\cos(84°-a)\sin(a+24°)$, you can use the trigonometric identity for the sine of a difference of angles:

$$\sin(A - B) = \sin(A)\cos(B) - \cos(A)\sin(B)$$

In this case, $A = 84°$ and $B = a+24°$. So, you can rewrite the expression as:

$$\sin(84°-a)\cos(a+24°)-\cos(84°-a)\sin(a+24°) = \sin(84°)\cos(a+24°) - \cos(84°)\sin(a+24°)$$

Now, you have a simpler expression. Depending on what you want to do next with this expression or if you have specific values for $a$, you can further simplify or evaluate it.