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The correct option is C [0, π4]∪[ 3π4, 3π2]The graph below represents |cos x| and sin x function. nbsp; From the graph, the required interval is nbsp;[0, ...

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Byju's Answer

Standard XII

Mathematics

Properties of Set Operation

x ∈ R:|cos x|...

Question

${x \in R : | cos x | \geq sin x} \cap [0, \frac{3 π}{2}] =$

[0, \frac{π}{4}] \cup [\frac{3 π}{4}, \frac{3 π}{2}]

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[0, \frac{π}{4}] \cup [\frac{π}{2}, \frac{3 π}{2}]

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[0, \frac{π}{4}] \cup [\frac{5 π}{4}, \frac{3 π}{2}]

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[0, \frac{3 π}{2}]

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Solution

The correct option is A $[0, \frac{π}{4}] \cup [\frac{3 π}{4}, \frac{3 π}{2}]$
The graph below represents $| cos x |$ and $sin x$ function.

From the graph, the required interval is $[0, \frac{π}{4}] \cup [\frac{3 π}{4}, \frac{3 π}{2}]$

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Similar questions

Q. The intervals for which

tan x > cot x

, where

x \in (0, π) - {\frac{π}{2}}

Q. A solution of the equation

\cos^{2} x + \sin x + 1 = 0

, lies in the interval
(a)

(- π / 4, π / 4)

(b)

(π / 4, 3 π / 4)

(c)

(3 π / 4, 5 π / 4)

(d)

(5 π / 4, 7 π / 4)

Q. The solution of the equation

\cos^{2} x + \sin x + 1 = 0

lies in the interval
(a)

(- π / 4, π / 4)

(b)

(π / 4, 3 π / 4)

(c)

(3 π / 4, 5 π / 4)

(d)

(5 π / 4, 7 π / 4)

Q. If

y = s i n^{- 1} x + t a n^{- 1} x + s e c^{- 1} x

, then set of values of y is

Q. A solution of the equation

\cos^{2} θ + \sin θ + 1 = 0

, lies in the interval
(a)

(- π / 4, π / 4)

(b)

(π / 4, 3 π / 4)

(c)

(3 π / 4, 5 π / 4)

(d)

(5 π / 4, 7 π / 4)

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{x∈R:|cos x|≥sin x}∩[0,3π2]=

The correct option is A [0,π4]∪[3π4,3π2]The graph below represents |cosx| and sinx function. From the graph, the required interval is [0,π4]∪[3π4,3π2]

${x \in R : | cos x | \geq sin x} \cap [0, \frac{3 π}{2}] =$

The correct option is A $[0, \frac{π}{4}] \cup [\frac{3 π}{4}, \frac{3 π}{2}]$
The graph below represents $| cos x |$ and $sin x$ function.

From the graph, the required interval is $[0, \frac{π}{4}] \cup [\frac{3 π}{4}, \frac{3 π}{2}]$