IfAngle 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 .

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

Applying componendo And dividendo,

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

Hence, proved.