tan_TF cos A = m cos B!2 m-

1.	tan_TF cos A = m cos B!2 m-
Answer» Given Cos A = m Cos B ⇒ Cos A / Cos B = m / 1. ( apply componendo and dividendo) ⇒ (Cos A + Cos B) / (Cos A - Cos B) = ( m + 1) / (m - 1) ⇒ {(2 Cos ( A+B) / 2 × Cos (A-B) / 2 } / {(- 2 Sin ( A+B) / 2 × Sin (A-B) / 2 } = ( m + 1) / (m - 1) ⇒ {(2 Cos ( A+B) / 2 × Cos (B - A) / 2 } / {( 2 Sin ( A+B) / 2 × Sin (B - A) / 2 } = ( m + 1) / (m - 1) ⇒ {( Cot ( A+B) / 2 × Cot (B - A) / 2 } = ( m + 1) / (m - 1) ⇒ {( Cot ( A+B) / 2 = { ( m + 1) / (m - 1) } Tan (B - A) / 2 Here x = ( m + 1) / (m - 1).

Answer»

Given Cos A = m Cos B

⇒ Cos A / Cos B = m / 1. ( apply componendo and dividendo)

⇒ (Cos A + Cos B) / (Cos A - Cos B) = ( m + 1) / (m - 1)

⇒ {(2 Cos ( A+B) / 2 × Cos (A-B) / 2 } / {(- 2 Sin ( A+B) / 2 × Sin (A-B) / 2 } = ( m + 1) / (m - 1)

⇒ {(2 Cos ( A+B) / 2 × Cos (B - A) / 2 } / {( 2 Sin ( A+B) / 2 × Sin (B - A) / 2 } = ( m + 1) / (m - 1)

⇒ {( Cot ( A+B) / 2 × Cot (B - A) / 2 } = ( m + 1) / (m - 1)

⇒ {( Cot ( A+B) / 2 = { ( m + 1) / (m - 1) } Tan (B - A) / 2

Here x = ( m + 1) / (m - 1).

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