Given that :

`sinx = 8/17`

We know that:

`sin^2 x + cos^2 x = 1 `

`==> cosx = sqrt(1-sin^2 x)= sqrt(1- 8^2/17^2) = 15/17`

==> `cosx = 15/17`

Now we will find the required identity.

==> We know that `sin2x = 2sinx cosx `

`==> sin2x = 2*8/17...

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Given that :

`sinx = 8/17`

We know that:

`sin^2 x + cos^2 x = 1 `

`==> cosx = sqrt(1-sin^2 x)= sqrt(1- 8^2/17^2) = 15/17`

==> `cosx = 15/17`

Now we will find the required identity.

==> We know that `sin2x = 2sinx cosx `

`==> sin2x = 2*8/17 * 15/17 = 240/17`

`==> cos2x = cos^2 x - sin^2 x = (15/17)^2 - (8/17)^2 = 161/289`

`==gt tan2x = (sin2x)/(cos2x)= (240/17)/(161/289)= (240*17)/(161) ~~ 25.34`