https://file.aiquickdraw.com/mathbot/file/172597912026632osn4jl.jpg

The equation in the image is:

\[
\sin(x) \cos(x) \cos(2x) = ?
\]

We can simplify this expression using trigonometric identities.

### Step-by-Step Simplification:

1. **Apply the double-angle identity for cosine:**

   \[
   \cos(2x) = 2\cos^2(x) - 1
   \]

   Substituting this into the equation:

   \[
   \sin(x) \cos(x) (2\cos^2(x) - 1)
   \]

2. **Distribute \(\sin(x)\cos(x)\):**

   \[
   = \sin(x)\cos(x)(2\cos^2(x)) - \sin(x)\cos(x)
   \]
   Simplify each term:

   \[
   = 2\sin(x)\cos^3(x) - \sin(x)\cos(x)
   \]

Thus, the simplified form of the expression is:

\

Learn how to simplify the trigonometric expression sin(x) cos(x) cos(2x) step-by-step using the double angle identity for cosine. This problem explores key trigonometric concepts and is suitable for students in Grades 10-12.

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