Answer:
24/25
Step-by-step explanation:
The usual form of the double-angle identity is for sine is ...
sin(2x) = 2sin(x)cos(x)
The cosine can be found from the sine using the Pythagorean identity ...
sin(x)² + cos(x)² = 1
cos(x) = √(1 -sin(x)²)
__
Filling in the given value for sin(x), we can find the cosine to be ...
cos(x) = √(1 -(4/5)²) = √(9/25) = 3/5 . . . . . . . assuming a first-quadrant angle
Then the desired sine is ...
sin(2x) = 2sin(x)cos(x) = 2(4/5)(3/5)
sin(2x) = 24/25
