Question

What is the value of tan⁡x given that sin⁡x+cos⁡x=1/5 and π/2<x<π ?

Answer 1

sinx+cosx = 1/5

square both sides and you have
sin(2x) = -24/25
so, cos(2x) = -7/25

Now you can use your half-angle formula for tan(x)