Question

$\sqrt{\sin ^2\left(-1\right)}\le 1-\sin \left(x\right)$

Answer 1

$\sqrt{sin^2\left(-1\right)}\le 1-sin\left(x\right)$

$\mathrm{Switch\:sides}$

$1-\sin \left(x\right)\ge \sqrt{\sin ^2\left(-1\right)}$

$\mathrm{Simplify\:}\sqrt{\sin ^2\left(-1\right)}:\quad \sin \left(1\right)$

$1-\sin \left(x\right)\ge \sin \left(1\right)$

$\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}$

$1-\sin \left(x\right)-1\ge \sin \left(1\right)-1$

$\mathrm{Simplify}$

$-\sin \left(x\right)\ge \sin \left(1\right)-1$

Answer 2

$\sf \to 1-\sin \left(x\right)\ge \sin \left(1\right)$

$\sf\to 1-\sin \left(x\right)-1\ge \sin \left(1\right)$

$\sf \to\red{-\sin \left(x\right)\ge \sin \left(1\right)}$