`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 (1)/(cos alpha * cos beta )+ tan alpha * tan beta = tan gamma , where 0 lt gamma lt (pi)/2 and alpha , beta are positive acute angles , show that (pi)/4 lt gamma lt (pi)/2

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

if abs({:(sinalpha, cosbeta), (cosalpha, sinbeta):})=1/2 , where alpha, beta are acute angles, then find the value of alpha+beta . a) pi/3 b) (2pi)/3 c) pi/2 d) pi/4

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 sinalpha-sinbeta=a and cosalpha+cosbeta=b then write the value of "cos"(alpha+beta) .

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

If sin alpha.sinbeta - cos alpha.cos beta+1=0 , then find the value of cot alpha.tan beta .

alpha + beta = 5 , alpha beta= 6 .find alpha - beta

sin alpha+ sinbeta=(1)/(4) and cos alpha+cos beta=(1)/(3) The value of tan (alpha+beta) is