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Question

If α, β are the roots of the equation tanx+secx=2cosx where x[0,2π), then the value of |αβ| is

A
2π3
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B
5π6
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C
2π5
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D
π2
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Solution

The correct option is A 2π3
tanx+secx=2cosx
sinx+1=2cos2x, x(2n+1)π2
2sin2x+sinx1=0
(2sinx1)(sinx+1)=0
sinx=12, sinx=1

sinx=1 not possible as x(2n+1)π2
sinx=12
x=π6,5π6
|αβ|=2π3

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