" 4.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 tan theta = ( tan alpha + tan beta)/(1 + tan alpha tan beta),"show that " sin 2 theta =(sin 2 alpha + sin 2 beta)/(1+sin 2 alpha sin 2 beta)

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 theta=(tan alpha+tan beta)/(1+tan alpha tan beta) then show that sin2 theta=(sin2 alpha+sin2 beta)/(1+sin2 alpha sin2 beta)