If `alpha,beta,gamma` are in A.P. show that `cot beta=(sin alpha-sin gamma)/(cos gamma-cos alpha)`

if alpha , beta , gamma are in A>P show that cot =(sinalpha-singamma)/(cosgammacosalpha)

If alpha, beta, gamma ,are positive acute angles and sin (alpha+beta-gamma)=cos(beta+gamma-alpha)=tan (gamma+alpha-beta)=1 find alpha,beta and gamma .

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 alpha, beta and gamma are angle such that tan alpha + tan beta+tan gamma= tan alpha tan beta tan gammaand x=cos alpha + I sin alpha, y=cos beta+ I sin beta and z= cos gamma+ I sin gamma, then the value of xyz is -

If alpha, beta, gamma are positive acute angles, prove that sin alpha+sin beta+ sin gamma gt sin (alpha+ beta+ gamma)

For all values of alpha,beta,gamma prove that: cos alpha + cos beta+ cos gamma+ cos(alpha+beta+gamma) ="4cos"(alpha+beta)/2cdot"cos" (beta+gamma)/2cdot"cos"(gamma+alpha)/2

If alpha and beta are complementary angles, then show that cot beta+cos beta= (cos beta)/(cos alpha) (1+sin beta) .

if 0ltalpha,beta,gamma lt(pi/2) prove that sin alpha+sin beta+sin gamma gtsin(alpha+beta+gamma)

If sec alpha = sec beta sec gamma+ tan beta tan gamma , then show that sec beta= sec gamma sec alpha+- tan gamma tan alpha .

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