Explanation

(b)
Given that, $\sin{\theta + \cos{\theta = 1}}$
$\Rightarrow \ \frac{1}{\sqrt{2\ }}\sin{\theta +}\frac{1}{\sqrt{2\ }}\cos{\theta = \frac{1}{\sqrt{2\ }}}$
$\Rightarrow \ \sin{\left( \ \theta + \frac{\pi}{4} \right) = \frac{1}{\sqrt{2\ }} = \sin\frac{\pi}{4}}$
$\Rightarrow \ \theta + \frac{\pi}{4} = n\pi + ( - 1)^{n}\frac{\pi}{4}\$
$\Rightarrow \ \theta = n\pi + ( - 1)^{n}\frac{\pi}{4} - \frac{\pi}{4}$