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

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

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 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.

Evaluate {:[( cos alpha cos beta , cos alpha sin beta , -sin alpha ),( -sin beta , cos beta, 0),( sin alpha cos beta, sin alpha sin beta, cos alpha ) ]:} =0

Evaluate {:|( cos alpha cos beta , cos alpha sin beta , -sin alpha ),( -sin beta , cos beta, 0),( sin alpha cos beta, sin alpha sin beta, cos alpha ) |:} =0

Evaluate {:[( cos alpha cos beta , cos alpha sin beta , -sin alpha ),( -sin beta , cos beta, 0),( sin alpha cos beta, sin alpha sin beta, cos alpha ) ]:} =0

Evaluate {:|( cos alpha cos beta , cos alpha sin beta , -sin alpha ),( -sin beta , cos beta, 0),( sin alpha cos beta, sin alpha sin beta, cos alpha ) |:} =1

If cos(alpha + beta) =0 , then sin (alpha- beta)= ________

Evaluate |[cos alpha cos beta, cos alpha sin beta, -sin alpha],[ -sin beta, cos beta, 0],[ sin alpha cos beta, sin alpha sin beta, cos alpha]|

Find the value of, cos alpha cos beta, cos alpha sin beta, -no alpha-sin beta, cos beta, 0 sin alpha cos beta, sin alpha sin beta, cos alpha] |