To simplify the expression \(\frac{2 \sin(x)}{1} \cdot \frac{\sin(x)}{\cos(x)}\), let’s go through each part step by step:

1. Simplify the first part: \(\frac{2 \sin(x)}{1}\) is simply \(2 \sin(x)\).
   
2. Substitute the expression, so we have:
   \[
   2 \sin(x) \cdot \frac{\sin(x)}{\cos(x)}
   \]

3. Combine terms by multiplying:
   \[
   \frac{2 \sin(x) \cdot \sin(x)}{\cos(x)} = \frac{2 \sin^2(x)}{\cos(x)}
   \]

4. Now, recall that \(\sin^2(x)\) can be written in terms of \(\tan(x)\) because \(\frac{\sin^2(x)}{\cos(x)} = \sin(x) \cdot \tan(x)\).

5. This gives us the simplified expression:
   \[
   2 \sin(x) \tan(x)
   \]

So, the simplified form is:
\[
2 \sin(x) \tan(x)
\]

Would you like more details on trigonometric simplifications? Here are some questions that may help deepen your understanding:

1. How can we further simplify expressions using trigonometric identities?
2. What are some common uses of the identity \(\sin^2(x) + \cos^2(x) = 1\)?
3. How does the identity \(\tan(x) = \frac{\sin(x)}{\cos(x)}\) assist in simplifying expressions?
4. What are other equivalent forms of \(\sin(x) \tan(x)\)?
5. How can we verify that two trigonometric expressions are equal?

**Tip:** Remember, using trigonometric identities can simplify complex expressions quickly, making it easier to work with equations involving trig functions.

Step-by-step solution for simplifying the trigonometric expression (2sin(x)/1)(sin(x)/cos(x)), utilizing trigonometric identities and simplification techniques. This solution covers concepts such as the Pythagorean identity and the tangent function. Ideal for high school students in Grades 10-12.

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