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Question

Number of solutions of the equation tan x + sec x = 2 cos x lying in the interval [0, 2π] is

A
1
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B
2
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C
3
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Solution

The correct option is B 2
The given equation can be written as
1+sinxcosx=2cosx
1+sinx=2cos2x=2(1sin2)x
2sin2x+sinx1=0
(1+sinx)(2sinx1)=0
sinx=1or12
Now sinx=1tanx and sec x not defined. Sinx=12x=π6or5π6.
The required number of solution is 2.

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