Question

If $\sin \theta+\cos \theta=1$, then the general value of $\theta$ is

(A) $2 n \pi$

(B) $n \pi+(-1)^n \frac{\pi}{4}-\frac{\pi}{4}$

(C) $2 n \pi+\frac{\pi}{2}$

(D) None of these

Answer 1

$\frac{1}{\sqrt{2}} \sin \theta+\frac{1}{\sqrt{2}} \cos \theta =\frac{1}{\sqrt{2}}$

$\Rightarrow \quad \sin \left(\theta+\frac{\pi}{4}\right)$ =\frac{1}{\sqrt{2}} 

$\Rightarrow \quad \theta  =n \pi+(-1)^n \frac{\pi}{4}-\frac{\pi}{4}$

So, The correct option will be (B).