If `0ltalphaltbetaltpi/2` show that `alpha-sin alpha lt beta-sinbeta`

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

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

If alpha + beta+gamma=pi , prove that sin^2 alpha + sin^ beta - sin^2 gamma = 2sinalpha sinbeta cosgamma

sin alpha sin beta-cos alpha cos beta=1 then show that tan alpha+tan beta=0

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)

If 0 lt alpha, beta lt pi and they satisfy cos alpha + cosbeta - cos(alpha + beta)=3/2

Let alpha, beta be such that pi lt alph-betalt3piif sin alpha+sinbeta=-21/65and cos alpha+cos beta =-27/65, then the value of cos""(alpha-beta)/(2), is

If cos(alpha-beta)+1=0, show that cos alpha+cos beta=0 and sin alpha+sin beta=0