Choose the correct option and justify your choice: 2tan30/(1+tan²30) = sin60, cos60, tan60, sin30

The correct option is A sin60
Given trigonometric expression is
2tan30/(1+tan²30)
We know that,
tan30 = 1/√3
∴ 2tan30/(1+tan²30) = 2(1/√3)/1+(1/√3)² = 2/√3 / 1+1/3 = 2/√3 / 4/3 = 6/(4√3) = √3/2
We know that,
sin60 = √3/2
∴ 2tan30/(1+tan²30) = sin60
Hence, option A is correct.