If angle `theta` is divided into two parts such that the tangents of one part is `lambda` times the tangent of other, and `phi` is their difference, then show that `sintheta=(lambda+1)/(lambda-1)sinphi` .

Explanation

Let

`A+B=theta;A−B=phi; and tanA=lambdatanB`

`∴(tanA)(tanB)=lambda`

Apply componendo and dividendo

`∴(tanA−tanB)/(tanA+tanB)=(lambda-1)/(lambda+1)`

or `(sin(A−B))/(sin(A+B))=(lambda−1)/(lambda+1)`

or `sinphi={(lambda−1)/(lambda+1)}sintheta`