Explanation:

Let's solve the given problem step by step:

Given Expression:

sin(5x - 25°) - cos(5y + 25°)

- Both (5x - 25°) and (5y + 25°) are acute angles.

Best Approach:

Recall that:

cos(?) = sin(90° - ?)

So, cos(5y + 25°) = sin(90° - (5y + 25°)) = sin(65° - 5y)

The expression becomes:

sin(5x - 25°) - sin(65° - 5y)

For this difference to be zero (and considering the acute angle conditions), set the two angles equal:

5x - 25° = 65° - 5y

=> 5x + 5y = 65° + 25°

=> 5x + 5y = 90°

=> x + y = 18°

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Answer Options:

1. 50°

2. 40°

3. 18°

4. 16°

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- Option 3 18° is correct.

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