[" If "alpha+beta=theta" and "(tan alpha)/(tan beta)=(x)/(y)," 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 : " prove that ", sin (alpha - beta) =(x-y)/(x+y) sin theta.

An angle theta is divided into two parts alpha, beta such that tan alpha: tan beta = x:y prove that sin (alpha-beta)=frac{x-y}{x+y}sin theta

if tan alpha-tan beta=x and cot beta-cot alpha=y prove that cot(alpha-beta)=(x+y)/(xy)

If tan beta=cos theta tan alpha , then prove that tan^(2)""(theta)/(2)=(sin(alpha-beta))/(sin(alpha+beta)) .

If tan beta=cos theta tan alpha , then prove that tan^(2)""(theta)/(2)=(sin(alpha-beta))/(sin(alpha+beta)) .

If tan beta=cos theta tan alpha , then prove that tan^(2)""(theta)/(2)=(sin(alpha-beta))/(sin(alpha+beta)) .

If tan beta=cos theta tan alpha , then prove that tan^(2)""(theta)/(2)=(sin(alpha-beta))/(sin(alpha+beta)) .

If (sin (theta- alpha))/(sin (theta- beta))=(x)/(y) and (cos (theta- alpha))/(cos(theta-beta))=(a)/(b) , then show that cos(alpha- beta)=(ax+by)/(bx+ay) .

If tan theta = ( tan alpha - tan beta)/(1-tan alpha tan beta),"show that", sin 2 theta=(sin 2 alpha- sin 2 beta)/(1- sin2 alpha sin 2 beta).

if tan beta=(n sin alpha cos beta)/(1-n sin^(2)alpha) then prove that tan(alpha-beta)=(1-n)tan alpha