The correct option is A 2√3
Let A (1, √3) and the triangle formed be OAB where O is origin.
B is the point of intersection of the tangent with the X axis.
The tangent of the circle x2+y2=a2 at (acosθ,asinθ) is xcosθ+ysinθ=a.
So the tangent at A (1,√3) is √3y+x=4 which intersects x axis at B(4,0).
The area af the triangle OAB is 2√3 sq.units.