CUET Preparation Today
Solve $|\sin x + \cos x| = |\sin x|+|\cos x|,\,x∈[0,2π]$. |
$[0,π/2]∪[π,3π/2]∪\{2π\}$ $[0,π/2]∪[1,3π/2]∪\{5π\}$ $[2,π/2]∪[π,π/2]∪\{π\}$ $[4,π/2]∪[π,π/2]∪\{4π\}$ |
$[0,π/2]∪[π,3π/2]∪\{2π\}$ |
The given relation holds only when sin x and cos x have the same sign or at least one of them is zero. Hence, $x∈[0,π/2]∪[π,3π/2]∪\{2π\}$ |
