If `sintheta+costheta=1/5and 0lethetaltpi" then "tantheta` is

Options

A. `-4//3`
B. `-3//4`
C. `3//4`
D. `4//3`

Answer

A

Explanation

`costheta+sintheta=1/5`
`rArr1+tantheta=1/5sectheta` (dividing by `costheta`)
`rArr25+50tan^2theta=sec^2theta`
`or12tan^2theta+25tan^2theta+12=0`
`or12tan^2theta+16tantheta+9tantheta+12=0`
`or (4tantheta+3)(3tantheta+4)=0`
`rArr tantheta=-3/4or tantheta=-4/3`
`tantheta=-3/4` is rejected
as then `costheta=-4/5and sintheta=3/5`
for which `costheta+sintheta=-1/5`
Hence, `tantheta=-4/3`