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Number of solutions of the equation tan ...

Number of solutions of the equation `tan x+sec x=2cos x` lying in the interval `[0,2 pi]` is

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

`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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