Find the exact value of the following expression (without using a calculator): tan(sin^-1 x/2)

tan(Sin^-1 x/2)=  

Step-by-step explanation:

Let sin^-1 x/2= θ

then sinθ= x/2

on the basis of unit circle, we have a triangle with hypotenuse of length 1,   one side of length x/2 and opposite angle of θ.

          tan(Sin^-1 x/2) = tanθ

           tanθ= sinθ/cosθ

as per trigonometric identities cosθ= √(1-sin^2θ)

           tanθ= sinθ/ √(1-sin^2θ)

substituting the value sinθ=x/2 in the above equation

             tanθ=

now substituting the value sin^-1 x/2= θ in above equation

             tan(sin^-1 x/2) =  

!

40 is the final : )