Question

how does 2cos(2x)-2cos(x)sin(x) becomes 2cos(2x)-sin(2x)?

Answer 1

To understand how the expression 2cos(2x)-2cos(x)sin(x) becomes 2cos(2x)-sin(2x), we need to apply trigonometric identities.

First, let's focus on the term -2cos(x)sin(x). We can use the following trigonometric identity:

sin(2x) = 2sin(x)cos(x)

By rearranging the terms in -2cos(x)sin(x), we have:

-2cos(x)sin(x) = sin(2x)

Now, substituting this into the original expression, we get:

2cos(2x) - 2cos(x)sin(x) = 2cos(2x) - sin(2x)

So, the expression 2cos(2x)-2cos(x)sin(x) simplifies to 2cos(2x)-sin(2x).