If `tanalpha=1/7,sinbeta=1/(sqrt(10)),` prove that`alpha+2beta=pi/4` , where `0

If cosalpha=1/(sqrt(2)),sinbeta=1/(sqrt(3)) , show that tan((alpha+beta)/2)cot((alpha-beta)/2)=5+2sqrt6 or 5-2sqrt6

sinalpha=1/(sqrt(10))*sinbeta=1/(sqrt(5)) (where alpha,beta and alpha+beta are positive acute angles). show that alpha+beta = pi/4

If sqrt2(sin alpha)/(sqrt(1+cos2 alpha))=1/7 and sqrt((1-cos2beta)/2)=1/(sqrt(10)) alpha, beta in (0, pi/2) then tan (alpha + 2 beta) is equal to _________

if alpha=(-1+sqrt(-3))/2 , beta=(-1-sqrt(-3))/2 then prove that alpha/beta+beta/alpha +1=0

If sinalpha=1/sqrt5 and sinbeta=3/5 , then beta-alpha lies in

If tanalpha =(1)/(7) and tanbeta =(1)/(3) , then, cos2alpha is equal to

If sin(alpha+beta)=1 and sin(alpha-beta)=1/2 , where 0lt=alpha, betalt= pi/2 , then find the values of tan(alpha+2beta) and tan(2alpha+beta) .

Let (sqrt(2)sin alpha)/sqrt(1+cos 2alpha)=1/7 and sqrt((1-cos2 beta)/2)=1/sqrt(10) where alpha,beta in (0,pi/2) . Then tan(alpha+2beta) is equal to

If (sqrt(2)cos alpha)/sqrt(1-cos2 alpha)=1/7 and sqrt((1+cos 2 beta)/2)=1/sqrt10,alpha,beta in (pi/2,pi) , then tan (2 alpha - beta) is equal to ........

If cosalpha+cosbeta=0=sinalpha+sinbeta , then prove that cos2alpha +cos2beta=-2cos(alpha +beta) .