(i) If cos α/cos β = m and cos α/sin β = n, then prove that (m^2 + n^2) cos^2 β = n^2 (ii) If cot θ + tan θ = x and sec θ - cos θ = y

Question

(i) If \(\frac{\cos\alpha}{cos\beta}\) = m and \(\frac{\cos\alpha}{sin\beta}\) = n, then prove that (m² + n²) cos² β = n²

(ii) If cot θ + tan θ = x and sec θ - cos θ = y then prove that \((x^2y)^{\frac{2}{3}}\,-\,(xy^2)^{\frac{2}{3}}\) = 1

Answer 1

(i) L.H.S.

(ii) x = cot θ + tan θ