Solve $|\sin x + \cos x| = |\sin x|+|\cos x|,\,x∈[0,2π]$.
Answer & explanation
Correct answer: option 1
The given relation holds only when sin x and cos x have the same sign or at least one of them is zero.
Hence, $x∈[0,π/2]∪[π,3π/2]∪\{2π\}$
Solve $|\sin x + \cos x| = |\sin x|+|\cos x|,\,x∈[0,2π]$.
Correct answer: option 1
The given relation holds only when sin x and cos x have the same sign or at least one of them is zero.
Hence, $x∈[0,π/2]∪[π,3π/2]∪\{2π\}$