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Question

Number of solutions of the equation tanx+secx=2cosx 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 D 3
tanx+secx=2cosx
sinx+1=2cos2xsinx+1=22sin2x
2sin2x+sinx1=0
(2sinx1)(sinx+1)=0
but sinx=1x=3π2 ...........(1)
sinx=12=sinπ6
therefore general solution is,
x=nπ+(1)n.π6
x=......,π6,5π6,...... ..........(2)
Therefore, number of solutions in the given interval are 3.
Hence, option 'D' is correct.

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