Which expression is equivalent to sin(2x)cos(x)
The expression equivalent to sin(2x)cos(x) can be found using the trigonometric identity: sin(2x) = 2sin(x)cos(x).
Using this identity, we can rewrite the expression as:
sin(2x)cos(x) = (2sin(x)cos(x))cos(x)
Simplifying further, we have:
sin(2x)cos(x) = 2(sin(x)cos(x)cos(x))
Finally, combining the terms with the same trigonometric function, we get:
sin(2x)cos(x) = 2sin(x)cos^2(x)
To find an expression equivalent to sin(2x)cos(x), we can use the trigonometric identity for the product of sine and cosine:
sin(2x)cos(x) = (sin(x)cos(x))(2sin(x))
Now, we can simplify further:
= 2sin(x)sin(x)cos(x)
= 2sin^2(x)cos(x)
Therefore, an expression equivalent to sin(2x)cos(x) is 2sin^2(x)cos(x).
recall your product-to-sum formulas, with
a = 2x
and
b = x
Now apply the formula for sina cosb
or, you can make it 2sinx cosx cosx and massage that to get one of your choices