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Given sec θ + csc θ = n ………………… (i) ⇒ 1/cos θ + 1/sin θ = n ⇒ (sin θ + cos θ)/cos θ sin θ = n cos θ sin θ = (sin θ + cos θ)/n sin θ = m/n, [using (i)] ………………… (ii) Now cos θ + sin θ = m ⇒ (cos θ + sin θ)2 = m2 ⇒ cos2 θ + sin2 θ + 2 sin θ cos θ = m2 ⇒ 1 + 2 sin θ cos θ = m2 ⇒ 1 + 2 ∙ (m/n) = m2, [Using (ii)] ⇒ 2 (m/n) = m2 - 1 ⇒ 2m = n(m2 - 1), [Proved]