Explanation

cosecθ−sinθ=cos²θ/sinθ=p³ and secθ−cosθ=sin²θ/cosθ=q³. Dividing: q³/p³=sin³θ/cos³θ=tan³θ, so tanθ=q/p, option B. A common error is to take the cube root carelessly and report p/q instead of q/p.