how does 2cos(2x)-2cos(x)sin(x) becomes 2cos(2x)-sin(2x)? Try to explain each step simply.

Answer 1

To understand how 2cos(2x) - 2cos(x)sin(x) becomes 2cos(2x) - sin(2x), let's break down the steps:

Step 1:
We have the expression 2cos(2x) - 2cos(x)sin(x).

Step 2:
Since sin(2x) = 2sin(x)cos(x), we can use this trigonometric identity to rewrite the expression as 2cos(2x) - sin(2x).

Step 3:
By replacing 2cos(x)sin(x) with sin(2x), we simplified the equation to its equivalent form.

Therefore, the expression 2cos(2x) - 2cos(x)sin(x) becomes 2cos(2x) - sin(2x) after applying the trigonometric identity.