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$I f 0 \leq x \leq 2 π a n d |\cos x| \leq \sin x, t h e n$

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x∈0,π4

x∈π4,2π

π4,3π4

0,π

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Correct option is C

We have cosx≤sinx⇒sinx≥0∵cosx≥0⇒x∉π,2πIf x∈(0,π2], then cosx≤sinx⇒cosx≤sinx ⇒x∈π4,π2 If x∈π2,π, then cosx≤sinx⇒-cosx≤sinx ∵cosx is negative ⇒tanx≤-1 ⇒x∈π2,3π4 ∴x∈π4,3π4

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If 0≤x≤2π and cosx≤sinx, then

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$I f 0 \leq x \leq 2 π a n d |\cos x| \leq \sin x, t h e n$