Sin * (x - y), if sin x = 8/17 cos y = 12/37

-429/629

Step-by-step explanation:

Use angle difference formula:

sin (x - y) = sin x cos y - sin y cos x

Assuming x and y are in the first quadrant:

sin (x - y) = sin x cos y - √ (1 - cos²y) √ (1 - sin²x)

Plugging in values:

sin (x - y) = (8/17) (12/37) - √ (1 - (12/37) ²) √ (1 - (8/17) ²)

sin (x - y) = (8/17) (12/37) - (35/37) (15/17)

sin (x - y) = - 429/629