Use the product-to-sum formula to write the given product as a sum or difference.
6sin π/10 cos π/ 10
look up your formulas. You want
2 sin(a) cos(b) = sin(a+b) cos(a-b)
You don't even need the product-to-sum formulas, since your double-angle formula says that
cos(2x) = 2 sinx cosx
Dang! That is
sin(2x) = 2 sinx cosx
that isn't one of my answers?
you telling me or asking me?
Naturally, sin(2x) is not one of your answers, but if you let x = π/10 and you plug that in, I bet it is one of your answers.
To use the product-to-sum formula to write the given product as a sum or difference, we first need to know the product-to-sum formula itself.
The product-to-sum formula is as follows:
sin(A) * cos(B) = (1/2) [sin(A + B) + sin(A - B)]
Now let's apply this formula to the given product:
6sin(π/10) * cos(π/10)
We can rewrite this as:
(1/2) [sin(π/10 + π/10) + sin(π/10 - π/10)]
Simplifying further:
(1/2) [sin(2π/10) + sin(0)]
Since sin(0) is equal to 0, we can simplify this to:
(1/2) [sin(π/5)]
Therefore, the given product 6sin(π/10) * cos(π/10) can be written as (1/2) * 6 * sin(π/5), or simply 3sin(π/5).