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

...