The equation given is:

\[
\sin \theta = \tan \theta
\]

We know that:

\[
\tan \theta = \frac{\sin \theta}{\cos \theta}
\]

Substituting this into the original equation:

\[
\sin \theta = \frac{\sin \theta}{\cos \theta}
\]

Now, multiply both sides by \(\cos \theta\) to eliminate the denominator:

\[
\sin \theta \cos \theta = \sin \theta
\]

If \(\sin \theta \neq 0\), we can divide both sides by \(\sin \theta\):

\[
\cos \theta = 1
\]

The solution to \(\cos \theta = 1\) is:

\[
\theta = 2n\pi \quad \text{(for any integer } n\text{)}
\]

Now, let's also consider the case where \(\sin \theta = 0\). This happens when:

\[
\theta = n\pi \quad \text{(for any integer } n\text{)}
\]

So, the general solution is:

\[
\theta = n\pi \quad \text{(for any integer } n\text{)}
\]

This includes both solutions: \(\theta = 0, \pi, 2\pi, 3\pi, \ldots\).

Would you like more details, or do you have any questions?

Here are 5 related questions:
1. What is the relationship between sine and tangent for other values of \(\theta\)?
2. How do we derive the general solution for trigonometric equations?
3. What happens if \(\sin \theta = 0\)?
4. How does the unit circle help in solving trigonometric equations?
5. What are the graphical interpretations of \(\sin \theta = \tan \theta\)?

**Tip:** Always check for special cases like \(\sin \theta = 0\) when solving trigonometric equations, as they might provide additional solutions.

Learn how to solve the trigonometric equation sin θ = tan θ using key trigonometric identities. This solution includes steps for cases when cos θ = 1 and sin θ = 0. Suitable for students in Grades 10-12 studying trigonometry.

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