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Tan A = n Tan B —(1)
Sin A = m Sin B — (2)
(2) ÷ (1) gives: CosA = (m/n) CosB –(3)
From (2)
Cos² A = 1 – m² Sin²B . [Cos² A+Sin² A=1]
= 1 – m² [1 – cos²B]
= 1 – m² + m² Cos²B
= 1 – m² + n² Cos²A using (3)
=> (n²-1) Cos²A = m² -1
=> Cos²A = (m² – 1) / (n² – 1)

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