prove that 1/2 tan -1 x = cos -1 ( 1 + root ( 1 + x2 )) / 2 root (1 + x2 ) ) 1/2

We need to prove that ....(1)

Substitute on the right hand side of the above equation.

Thus, we have,

Now consider the left side of the equation and substitute

Thus from equations (2) and (3), Left hand side of the equation (1) is equal to the right hand side of the equation (1).

Hence proved.

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