An angle theta is divided into two parts alpha and beta such that tan alpha : tan beta = x:y then prove that sin (alpha-beta) =

x-y / x+y sin theta.

Question

An angle theta is divided into two parts alpha and beta such that
tan alpha : tan beta = x:y then prove that sin (alpha-beta) =

x-y / x+y sin theta

Anuradha Sharma · Accepted Answer

tanα:tanβ=x:y tanαtanβ=xy
1Also, θ=α+β
2Using componendo -divindo to equation 1, tanα+tanβtanα-tanβ=x+yx-yx-yx+y= tanα-tanβtanα+tanβ=sinαcosβ-cosαsinβsinαcosβ+cosαsinβ=sinα-βsinα+β=sinα-βsinθ Using equation 2So we get sinα-β=x-yx+ysinθ

An angle theta is divided into two parts alpha and beta such that tan alpha : tan beta = x:y then prove that sin (alpha-beta) = x-y / x+y sin theta.

An angle theta is divided into two parts alpha and beta such that tan alpha : tan beta = x:y then prove that sin (alpha-beta) =

x-y / x+y sin theta.