Which expression is equivalent to sin(2x)cosx
To find the equivalent expression to sin(2x)cosx, we can use the double-angle identity for sine and the identity for cosine.
1. Double-angle identity for sine: sin(2x) = 2sin(x)cos(x)
Now let's substitute this identity into our expression:
sin(2x)cos(x) = (2sin(x)cos(x))(cos(x))
To simplify further, we can use the identity for cosine:
cos(α)cos(β) = (1/2)(cos(α + β) + cos(α - β))
Using this identity, we can rewrite the expression as:
(2sin(x)cos(x))(cos(x)) = (2sin(x)cos^2(x)) = (2sin(x))(cos^2(x))
Therefore, the equivalent expression to sin(2x)cos(x) is 2sin(x)cos^2(x).