Let's complete the proof using trigonometric identities.
We need to show that:
[tex]\[
\cos (\theta) \cdot \tan (\theta) = \sin (\theta)
\][/tex]
First, recall the definition of the tangent function in terms of sine and cosine:
[tex]\[
\tan (\theta) = \frac{\sin (\theta)}{\cos (\theta)}
\][/tex]
Next, substitute this expression for [tex]\(\tan (\theta)\)[/tex] into the left-hand side of the equation:
[tex]\[
\cos (\theta) \cdot \tan (\theta) = \cos (\theta) \cdot \left( \frac{\sin (\theta)}{\cos (\theta)} \right)
\][/tex]
We can simplify this by canceling [tex]\(\cos (\theta)\)[/tex] from the numerator and the denominator:
[tex]\[
\cos (\theta) \cdot \left( \frac{\sin (\theta)}{\cos (\theta)} \right) = \sin (\theta)
\][/tex]
Therefore, we have shown that:
[tex]\[
\cos (\theta) \cdot \tan (\theta) = \sin (\theta)
\][/tex]
And this completes the proof.
