Question

If Angle θ is divided into two parts such that the tangents of the one part is λ times the tangent of other, And ϕ is their difference, then show that sin θ  = \(\frac{λ+1}{λ-1}\)sin ϕ

Answer 1

Let α And β be the two parts of angle θ. 

Then, given θ = α + β And ϕ = α - β 

Consider tan α = λ tan β

⇒ \(\frac{tanα}{tanβ}\) = \(\frac{ λ}1\)

Applying componendo And dividendo,

We know that sin(A ±B) = sinA cosB ± cosA sinB

Hence, proved.