`(sinalpha+sinbeta-sin(alpha+beta))/(sinalpha+sinbeta+sin(alpha+beta))=tan(alpha/2)tan(beta/2)`

If 3sinbeta=sin(2alpha+beta) then

sinalpha+sinbeta=a ,cosalpha+cosbeta=b=>sin(alpha+beta)

Sum the series tan alpha tan (alpha+beta)+tan(alpha+beta)+tan(alpha+2beta)+tan(alpha+2beta)tan(alpha+3beta)+… to n terms

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

If alpha,beta in (-pi/2,0) such that (sin alpha+sinbeta)+(sinalpha)/(sinbeta)=0 and (sinalpha+sinbeta) (sinalpha)/(sinbeta)=-1 and lambda=lim_(n->oo) (1+(2sinalpha)^(2n))/((2sinbeta)^(2n)) then :

If sinalpha+sinbeta=a ,cosalpha+cosbeta=b=>sin(alpha+beta) =

If A=[(0,sin alpha, sinalpha sinbeta),(-sinalpha, 0, cosalpha cosbeta),(-sinalpha sinbeta, -cosalphacosbeta, 0)] then (A) |A| is independent of alpha and beta (B) A^-1 depends only on beta (C) A^-1 does not exist (D) none of these

Evaluate |(cosalphacosbeta,cosalpha sinbeta , - sin alpha),(-sin beta,cosbeta,0),(sinalphacosbeta,sinalpha sinbeta,cosalpha)|

Show that (sin (alpha + beta))/( sin (alpha + beta)) = 2, given that tan alpha = 2 tan beta.

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