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

If cos (beta - gamma) + cos (gamma - alpha) + cos (alpha - beta) = -3/2, "show that", cos alpha + cos beta + cos gamma = 0 "and" sin alpha + sin beta + singamma = 0."Hence deduce that," cos (beta - gamma) = cos (gamma - alpha) = cos (alpha - beta) = -1/2.

If sin alpha sin beta - cos alpha cos beta + 1 = 0,"show that", sin (alpha + beta) = 0, "hence deduce that," 1 + cot alpha tan beta = 0.

If sin alpha = sin beta and cos alpha = cos beta then-

sin alpha + sin beta = a "and" cos alpha + cos beta = b sin (alpha + beta) =

If a sin alpha = b sin beta " then show that ", b cot alpha + a cot beta = (a+b) "cot"(alpha+beta)/2

If cot alpha cot beta = 3,"show that", (cos (alpha - beta))/(cos (alpha + beta)) =2

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

sin alpha + sin beta = a "and" cos alpha + cos beta = b cos (alpha + beta) =

cos(beta-gamma)+cos(gamma-alpha)+cos(alpha-beta)=-3/2 show that cosalpha+cosbeta+cosgamma=0 and sinalpha+sinbeta+singamma=0 also cos(beta-gamma)=cos(gamma-alpha)=cos(alpha-beta)=-1/2 .

If sin 2 alpha + sin 2 beta = 3 "and" cos 2 alpha + cos 2 beta = 4,"then"- sin 2 ( alpha + beta)