\(\displaystyle{ -|\cos 100^{\circ}|\sqrt{1+\tan^2 100^{\circ}} =-\sqrt{\cos^2 100^{\circ}(1+\tan^2 100^{\circ})}=-\sqrt{\cos^2 100^{\circ}+\tan^2 100^{\circ} \cdot \cos^2 100^{\circ}}= \\
-\sqrt{\cos^2 100^{\circ}+\frac{\sin^2 100^{\circ}}{\cos^2 100^{\circ}} \cdot \cos^2 100^{\circ}}}\)