Question

If $|\sin x+\cos x|=|\sin x|+|\cos x|$, where $\sin x\ne 0,\cos x\ne 0$, then in which quadrant does $x$ lie?

• A. $\text{Quadrant I}$
• B. $\text{Quadrant II}$
• C. $\text{Quadrant III}$
• D. $\text{Quadrant IV}$

Answer 1

Answer: (A), (C)

The correct options are
A $\text{Quadrant I}$
C $\text{Quadrant III}$

Here we have $|\sin x+\cos x|=|\sin x|+|\cos x|$.
It implies that $\sin x$ and $\cos x$ must have the same sign.
Therefore, $x$ lies in the first or third quadrant.