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

If 3 sin alpha=5 sin beta , then (tan((alpha+beta)/2))/(tan ((alpha-beta)/2))=

If the eccentric angles of the extremities of a focal chord of an ellipse x^2/a^2 + y^2/b^2 = 1 are alpha and beta , then (A) e = (cos alpha + cos beta)/(cos (alpha + beta)) (B) e= (sin alpha + sin beta)/(sin(alpha + beta)) (C) cos((alpha-beta)/(2)) = e cos ((alpha + beta)/(2)) (D) tan alpha/2.tan beta/2 = (e-1)/(e+1)

If cos(alpha+beta)=0 then sin(alpha+2beta)=

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

If "sin" alpha=ksinbeta then tan((alpha-beta)/(2)).cot((alpha+beta)/(2)) is equal to

lf cos^2 alpha -sin^2 alpha = tan^2 beta , then show that tan^2 alpha = cos^2 beta-sin^2 beta .

Show that: sin^2 alpha + sin^2 beta + 2sinalpha sinbeta cos(alpha+beta)=sin^2 (alpha+beta)

If sin (alpha + beta) = 4/5 , sin (alpha -beta) = (5)/(13), alpha + beta , alpha - beta being acute angles prove that tan 2 alpha = (63)/(16).

If (tanalpha+tanbeta)/(cot alpha+cot beta)+{cos(alpha-beta)+1}^(-1)=1, then tan alpha tan beta is equal to

Given that sin beta =(4)/(5), 0 lt beta lt pi and tan beta gt 0, " then " ((3 sin(alpha+beta)-4 cos (alpha+beta))"cosec"alpha is equal to :