Answer:
tan(Sin^-1 x/2)= [tex]\frac{x/2}{\sqrt{1-x^{2}/4 } }[/tex]
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= [tex]\frac{x/2}{\sqrt{1-x^{2}/4 } }[/tex]
now substituting the value sin^-1 x/2= θ in above equation
tan(sin^-1 x/2) = [tex]\frac{x/2}{\sqrt{1-x^{2}/4 } }[/tex]
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