Explanation:
what do you mean :
cos(2A) = 7/25
or
cos²(A) = 7/25
?
if it is the first :
cos(2A) = 1 - 2×sin²(A)
7/25 = 1 - 2×sin²(A) = 25/25 - 2×sin²(A)
-18/25 = -2×sin²(A)
9/25 = sin²(A)
3/5 = sin(A)
correct
just in case, if it would have been the second :
cos²(A) + sin²(A) = 1
cos²(A) = 1 - sin²(A)
7/25 = 1 - sin²(A) = 25/25 - sin²(A)
-18/25 = -sin²(A)
18/25 = sin²(A)
sin(A) = sqrt(18)/5 = sqrt(9×2)/5 = 3×sqrt(2)/5
this is NOT 3/5.
so, this would be wrong, and clearly you meant the first option.