If secθ−tanθ=1.5 , then θ  lies in the quadrant

secθ−tanθ=32                 ⇒secθ+tanθ=23                (add)     2secθ=32+23=136                ⇒secθ=1312>0  ----- (1)                (substract) −2tanθ=32−23=56                   ⇒tanθ=−512<0  ---- (2)                From (1) & (2) θ∈IV quadrant