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The number of solutions of the equation ...

The number of solutions of the equation sin2x-2cosx+4sinx=4 in the interval `[0,5pi]` is

A

3

B

5

C

4

D

6

Text Solution

Verified by Experts

The correct Answer is:
A
`sin2x-2cosx+4sinx=4`
`rArr2sinxcosx-2cosx+4sinx=4`
`rArr(sinx-1)(2cosx+4)=0`
`rArrsinx=1,cosxne-2`
`thereforex=npi+(-1)^(n)(pi)/(2)`, where n =0,1,2,…5
Here , the required value of `x=(pi)/(2),(5pi)/(2)(9pi)/(2)` in interval `[0,5pi]`
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