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Question

The number of solutions of the equation |cosxsinx|=2cosx, xϵ[0,2π] is


A

1

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B

2

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C

3

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D

4

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Solution

The correct option is B

2


Three cases can be considered:

(i) cosx=sinx=0 which is impossible

(ii) cosx>sinx, 0x<π4 and 5π4<x2π

2cosx=cosxsinx

tanx=1x=7π4

(iii) cosx<sinxπ4<x<5π4

then x=tan13

So, there are 2 solutions.


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