If 1 + sinθ = x cosθ, then cotθ is-

Question: If 1 + sinθ = x cosθ, then cotθ is-Solution:Given,1+ sinθ = xcos θ⇒ (1 + sinθ)/cosθ = x⇒ 1/cosθ + sinθ/cosθ = x⇒ secθ + tanθ = x...............(i)We know, sec2θ - tan2θ = 1⇒ (secθ + tanθ) (secθ - tanθ) = 1 ⇒ x(secθ - tanθ) = 1⇒ secθ - tanθ = 1/x.................(ii)(i) - (ii) ⇒secθ + tanθ - (secθ - tanθ) = x - 1/x⇒ secθ + tanθ - secθ + tanθ = (x2 - 1)/x⇒ 2tanθ = (x2 - 1)/x⇒ tanθ = (x2 - 1)/2x∴ cotθ = 2x/(x2 - 1)