If tana = n tan Band sin A = m sin B, prove that Cos² A = m² – 1/ n² – 1

Hint: On simplification we get, cosA = mcosB/n.
Now since cos²A = 1-sin²A = 1-m²(1-cos²B) = 1 – m² + n²cos²A.
On simplification, we will get cos²A = (m²-1)/(n²-1). Thanks