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Question

The number of solutions of the equation tanx+secx=2cosx in the interval [0,2π] is

A
1
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B
2
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C
3
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D
4
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Solution

The correct option is B 2
tanx+secx=2cosx
sinxcosx+1cosx=2cosx
sinx+1=2cos2x for cosx0
sinx+1=22sin2x2sin2x+sinx1=0(2sinx1)(sinx+1=0)
sinx=12
or sinx=1 (not possible as then cosx=0 and secx, tanx are not defined.)
x=π6,5π6
Hence, number of solutions =2

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