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The number of solution of cosx=|1+sinx|,...

The number of solution of `cosx=|1+sinx|,0lexle3pi` is

A

2

B

3

C

4

D

5

Text Solution

Verified by Experts

The correct Answer is:
B
Clearly , `1+sinxge0`
`therefore` The given equation becomes
cosx-sinx=1
`rArr(1)/(sqrt(2))cosx-(1)/(sqrt(2))sinx=(1)/(sqrt(2))`
`rArr"cos"(pi)/(4)"cos x-sin"(pi)/(4)"sinx"=(1)/(sqrt(2))`
`rArrcos(x+(pi)/(4))=(1)/(sqrt(2))`
`x+(pi)/(4)=(pi)/(4),(7pi)/(4),(9pi)/(4),(15pi)/(4)`, ...
`rArrx=0,(3pi)/(2),2pi,(7pi)/(2)`, ...
For `0lexle3pi`
`x=0,(3pi)/(2),2pi`
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