If |cos x + sin x| + |cos x - sin x| = 2 sin x ; x ∈ [0,2 π ] , then maximum integral value

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Trigonometrical Equations

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If $|cos\ x + sin\ x| + |cos\ x\ -\ sin\ x| = 2\ sin\ x$ ; $x \in [0,2 \pi ]$ , then maximum integral value of $x$ is

A

$1$

B

$2$

C

$3$

D

$4$

Solution

$\cos x\, + \,\sin \,x\, \geqslant \,0\,\ \,\cos \,x\, – \,\sin \,x\, \leqslant \,0$

$ \Rightarrow \,\left[ {\frac{\pi }{4},\frac{{3\pi }}{4}} \right]$

Standard 11

Mathematics

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