If `tan beta = 3 tan alpha,` prove that `tan (alpha + beta) = (2sin 2beta)/(1+cos 2beta)`

If tan (alpha-beta)=(sin 2beta)/(3-cos 2beta) , then

If 2\ t a nalpha=3t a nbeta, prove that tan(alpha-beta)=(sin2beta)/(5-cos2beta)

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

(1+tan alpha tan beta)^2 + (tan alpha - tan beta)^2 =

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

If a right angle be divided into three parts alpha, beta and gamma , prove that cot alpha = (tan beta + tan gamma)/(1-tan beta tan gamma) .

Prove that: tan(alpha+beta)tan(alpha-beta)=(sin^2 alpha-sin^2 beta)/(cos^2 alpha-sin^2 beta)

If 2 tan (alpha/2)=tan (beta/2), prove that cos alpha=(3+5 cos beta)/(5+3 cos beta).

if tan alpha = 2tanbeta show that (sin(alpha+beta))/(sin(alpha-beta)) = 3

If sin alpha + sin beta = a and cos alpha + cos beta = b, prove that : cos (alpha-beta) = 1/2 (a^2 + b^2 -2)