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`.

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

If cos beta cos (gamma- alpha)= cos (alpha- beta+ gamma) , prove that cot alpha+ cot y= 2cot beta

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 + sin gamma =3, then the value of (cos alpha + cos beta+ cos gamma) is-

If (cosalpha+cosbeta+cosgamma)=0, sinalpha+sinbeta+singamma=0 then show that cos3alpha+cos3beta+cos3gamma=3cos(alpha+beta+gamma)

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

If |{:(1,cos alpha, cos beta),(cos alpha, 1 , cos gamma ),(cos beta, cos gamma , 1):}|=|{:(0,cos alpha, cos beta),(cos alpha , 0 , cos gamma),(cos beta, cos gamma, 0):}| then the value of cos^2 alpha + cos^2 beta + cos^2 gamma is : (a) 1 (b) 1/2 (c) 3/8 (d) 9/4

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

Express cos alpha + cos beta + cos gamma+ cos ( alpha+beta+gamma) as the product of three cosines.

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