The value of `sin(2\ (tan^(-1)0. 75))` is equal to (a) 0.75 (b) 1.5 (c) 0.96 (d) `sin^(-1)1. 5`

Explanation

We have given

`sin(2\ tan^(-1)0. 75)`

`=sin(2\ tan^(-1)(75/100))`

`sin(2\ tan^(-1)(3/4))`

As we know that

`2tan^(−1)x=sin^(−1)((2x)/(1+x^2))`

Then

`sin(2\ tan^(-1)(3/4))=sin(sin^(-1)((2\times(3/4))/(1+(3/4)^2)))`

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