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Question

The number of solutons of the equation tan x +sec x = 2cos x lying in the interval [0,2π] is


A

0

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B

1

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C

2

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D

3

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Solution

The correct option is C

2


The given equation is
tan x +sec x =2 cos x
or sinxcosx+1cosx=2cosx
or sinx+1=2cos2x=22sin2x
or 2sin2x+sinx1=0
or (2 sinx-1)(sin x+1)=0
or sinx=12,1
x=π6,5π6,3π2[0,2π]
But for x=3π2, tan x and sec x are not defined.
Therefore, there are only two solutoins.


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