Q32 of 90 Page 7

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.


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