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The total number of solutions of cos x= ...

The total number of solutions of `cos x= sqrt(1- sin 2x)` in `[0, 2pi]` is equal to

A

2

B

3

C

5

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`becausecosx=sqrt(1-sin2x)`
`rArrcosx=sqrt((sinx-cosx)^(2))`
`rArrcosx=|sinx-cosx|`
Therefore are two cases arise.
Case I When `sinxlecosx`, then
`rArrx in[0,(pi)/(4)]uu((5pi)/(4),2pi]`
cos x =cos x-sinx
`rArrsinx=0`
`rArrx=2pi[becausex=pinotin(0,(pi)/(4))uu((5pi)/(4),2pi)]`
Case II `sinxgtcosxrArrx in((pi)/(4),(5pi)/(4))`, then
cos x = sin x - cosx
`rArrtanx=2`
`becausetanx=2rArrx=tan^(-1)(2)`
Thus ,the given equation has solutions.
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