secθ−tanθ=x (1)
sec2θ−tan2θ=1 (2)
(2)÷(1)
sec2θ−tan2θsecθ+tanθ=1x
secθ+tanθ=1x (3)
Adding (1) & (3)
2secθ=x+1x
secθ=12(x+1x)
Substract (3) – (1)
2tanθ=1x−x
tanθ=12(1x−x)