\( \left[\sin ^{2} \theta\right. \) can be written a (a) \( \sin ^{2} 230^{\circ} \)

It appears that your question is incomplete or partially provided. However, based on the information given, I can offer some insights into expressing \(\sin^2 \theta\) using trigonometric identities. ### Expressing \(\sin^2 \theta\) One common way to express \(\sin^2 \theta\) is by using the **double-angle identity** for sine: \[ \sin^2 \theta = \frac{1 - \cos(2\theta)}{2} \] This identity is useful in various applications, including integration and simplifying trigonometric expressions. ### Regarding \(\sin^2 230^\circ\) If the question involves expressing \(\sin^2 \theta\) as \(\sin^2 230^\circ\), it typically would imply a specific angle substitution rather than a general identity. For example: \[ \sin^2 \theta = \sin^2 230^\circ \quad \text{if} \quad \theta = 230^\circ + k \cdot 180^\circ \quad \text{for any integer } k \] This is because the sine function has a period of \(180^\circ\) when squared, meaning: \[ \sin^2 \theta = \sin^2 (\theta + 180^\circ) \] ### Next Steps If you have multiple options (like (a), (b), etc.) or additional parts of the question, please provide them so I can offer a more accurate and comprehensive answer. Feel free to share the complete question or any specific aspect you'd like assistance with!