Write an algebraic expression that is equivalent to sin tan1

Write an algebraic expression that is equivalent to sin (tan^-1 x/2). 2/Squarerootx ^2+4 x/Squarerootx ^2+4 Squareroot x^2+4/x Squareroot x^2+4/x

Solution

sin ( tan^-1 x / 2 )

let

( tan^-1 x / 2 ) = y

tan y = x/2

perpendicular = x

base = 2

hypotenuse = sqrt ( x^2 + 2^2 ) = sqrt ( x^2 + 4 )

sin y = x / sqrt ( x^2 + 4)

or

sin ( tan^-1 x / 2 ) = x / sqrt ( x^2 + 4)

option b is correct