If `sin alpha sin beta-cosalphacosbeta+1=0,` then prove that `1+cotalphatanbeta=0`

If sinalphasinbeta-cosalphacosbeta+1=0, then prove that 1+cotalphatanbeta=0

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

If sin alpha + sin beta = a and cos alpha + cos beta = b, prove that : cos (alpha-beta) = 1/2 (a^2 + b^2 -2)

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

If cos alpha+ cos beta =1/3 and sin alpha+sin beta=1/4 prove that cos[(alpha-beta)/2] =+-(5/24)

If cosalpha+cosbeta+cosgamma=0 a n d a l so sinalpha+sinbeta+singamma=0, then prove that cos2alpha+cos2beta+cos2gamma =sin2alpha+sin2beta+sin2gamma=0 sin3alpha+sin3beta+sin3gamma=3sin(alpha+beta+gamma) cos3alpha+cos3beta+cos3gamma=3cos(alpha+beta+gamma)

If cos alpha + cos beta + cos gamma = 0 and also sin alpha + sin beta + sin gamma= 0, then prove that: cos 3 alpha + cos 3beta + cos 3gamma = 3 cos (alpha + beta + gamma)

If m sin (alpha+beta) = cos (alpha-beta) , prove that (1)/(1- m sin 2 alpha)+(1)/(1-m sin 2 beta)=(2)/(1-m^(2)) .

If sin alpha, sin beta and cos alpha are in GP, then roots of x^2 + 2x cot beta + 1 = 0 are always