$\cos \theta+\sin \theta =\sqrt 2(\large\frac{1}{\sqrt 2}$$\cos \theta+\large\frac{1}{\sqrt 2}$$\sin \theta)$
Multiplying and dividing by $\sqrt{1^2+1^2}$ (i.e) by $\sqrt 2$
$\Rightarrow \sqrt 2(\cos\theta\cos\large\frac{\pi}{4}$$+\sin \theta\sin \large\frac{\pi}{4})$
$\Rightarrow \sqrt 2\cos(\theta-\large\frac{\pi}{4})=$$\sqrt 2\cos(100^{\large\circ}-45^{\large\circ})$
$\Rightarrow \sqrt 2\cos 55^{\large\circ}$
$\Rightarrow$ a positive quantity $(\cos 55^{\large\circ} > 0)$