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We need to find the value of sin (2(tan^-1 0.75)).

We can re-write the equation,

sin (2(tan^-1 0.75)) = sin (2 tan^-1 0.75)

Using the property of inverse trigonometry,

Replace x by 0.75.

So,

sin (2(tan^-1 0.75)) = sin (2 tan^-1 0.75)

⇒ sin (2(tan^-1 0.75)) = sin (sin^-1 0.96)

Using the property of inverse trigonometry,

sin(sin^-1 A) = A

⇒ sin (2(tan^-1 0.75)) = 0.96