First slide

Algebra of real valued functions

Question

If $|\sin x + \cos x| = |\sin x| + |\cos x|,$ then x lies in

Moderate

A

1st quadrant only
B

1st and 3rd quadrant only
C

2nd and 4th quadrant only
D

3rd and 4th quadrant only

Solution

The given relation holds only when sin x and cos x have same sign or at least one of them is zero.
hence $x \in [0, π / 2] \cup [π, 3 π / 2]$

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