If `0ltxltpiand cosx+sinx=1/2,` then tan x is equal to

Options

A. `(1-sqrt7)/(4)`
B. `(4-sqrt7)/(3)`
C. `(4+sqrt7)/(3)`
D. `(sqrt7+1)/(4)`

Answer

C

Explanation

We have,
`cosx+sinx=1/2`
`implies(cosx+sinx)^(2)=1/4`
`1+sin2x=1/4`
`impliessin2x=-3/4`
`implies3tan^(2)x+8tanx+3=0impliestanx=(-4+-sqrt7)/(3)`
Hence, option (c ) is correct.