Question

if tan ( alpha+ theta)=n tan (alpha-theta)
prove that:-
sin 2 theta /sin 2 alpha=n-1/n+1​

Answer 1

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Answer 2

Answer:

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Step-by-step explanation:

an(α+θ)=ntan(α−θ)

⇒tan(α+θ)/tan(α−θ)=n1

Using componendo and dividendo,

⇒tan(α+θ)+tan(α−θ)/tan(α+θ)−tan(α−θ)=n+1n−1

⇒sin(α+θ)cos(α+θ)+sin(α−θ)cos(α−θ)sin(α+θ)cos(α+θ)−sin(α−θ)cos(α−θ)=n+1n−1

⇒sin(α+θ)cos(α−θ)+cos(α+θ)sin(α−θ)sin(α+θ)cos(α−θ)+cos(α+θ)sin(α−θ)=n+1n−1

⇒sin(α+θ+α−θ)sin(α+θ−α+θ)=n+1n−1

⇒sin2αsin2θ=n+1n−1

⇒(n−1)sin2α=(n+1)sin2θ.