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

Options

A. 0
B. 1
C. 2
D. 3

Explanation

`tanx+secx = 2cosx`

`=>sinx/cosx +1/cosx = 2cosx`

`=>1+sinx = 2cos^2x`

`=>1+sinx = 2(1-sin^2x)`

`=>1+sinx = 2- 2sin^2x`

`=>2sin^2x+sinx-1 = 0`

`=>2sin^2x+2sinx-sinx-1 = 0`

`=>2sin(sinx+1)-1(sinx+1) = 0`

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