If tangent of x is equal to 3 fifths and sine of x is greater than 0 , what is sine of 2 x ?

Use the double-angle identity: sin(2x) = 2 tan(x) / (1 + tan²(x)). Substituting tan(x) = 3/5 gives sin(2x) = 2(3/5) / (1 + 9/25) = (6/5) / (34/25) = 30/34. Thus the answer is 30 over 34. The condition sin(x) > 0 is consistent with the positive tangent, but the identity already determines the result.

AI-written and checked against the verified answer.