Question

If tan α = n tan β and sin α = m sin β then cos2α is

Answer 1

Sol: Given tan α = n tan β ⇒ 1 / tan β = n / Tan α ⇒ Cot β = n Cos α / Sin α -------------(1) Also Sin α= m Sin β, ⇒ 1 / Sin β = m / Sin α ⇒ Cosec β = m / Sin α -------------(2) We know that Cosec2 β - Cot2 β = 1 ⇒ (m2 / Sin2 α) - (n2 Cos2 α / Sin2 α) = 1 [ from (1) and (2) ] ⇒ (m2 - n2 Cos2 α / Sin2 α) = 1 ⇒ (m2 - n2 Cos2 α ) = Sin2 α ⇒ (m2 - n2 Cos2 α ) = 1 - Cos2 α ⇒ (m2 - 1 ) = (n2 Cos2 α - Cos2 α) ⇒ (m2 - 1 ) = (n2 - 1) Cos2 α ∴ cos2 α = (m2-1) /( n2-1)

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Answer 2

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