It looks like you've uploaded an image containing a series of trigonometric identities and proofs. Each section asks to prove specific identities given certain conditions, such as $A + B + C = \pi$ or $\alpha + \beta + \gamma = \frac{\pi}{2}$.

Would you like to focus on solving one particular problem from this image? If so, please let me know which one, and I can guide you through the solution.

Alternatively, if you want a detailed breakdown of the steps for proving a specific identity or all of them, I can provide that as well.

Questions to Explore:

1. Would you like to start with proving one specific identity, such as the one in question 1(a)?
2. Do you need an explanation of trigonometric identities that can be used for these proofs?
3. Are there any particular identities here that seem unclear or confusing to you?
4. Do you need help understanding how the condition $A + B + C = \pi$ influences the trigonometric identities?
5. Would you like to see how these identities are applied in practical problems?

Tip:

When proving trigonometric identities, start by expressing complex trigonometric functions in terms of simpler ones like sine and cosine. This often simplifies the proof process.