#### Answer

$4\sin x$

#### Work Step by Step

$\left( \sin x+1\right) ^{2}-\left( \sin x-1\right) ^{2}=\left( \left( \sin x+1\right) -\left( \sin x-1\right) \right) \left( \left( \sin x+1\right) +\left( \sin x-1\right) \right) =2\times \left( 2\sin x\right) =4\sin x$