Prove that: `|(sinalpha, cosalpha, 1),(sinbeta, cosbeta, 1),(singamma, cosgamma, 1)|=sin(alpha-beta)+sin(beta-gamma)+sin(gamma-alpha)`

cos alpha sin (beta-gamma) + cos beta sin (gamma-alpha) + cos gamma sin (alpha-beta) =

Prove that: sin alpha+sin beta+sin gamma-sin(alpha+beta+gamma)=4sin((alpha+beta)/(2))*sin((beta+gamma)/(2))*sin((gamma+alpha)/(2))

Prove that: sin alpha+sin beta+sin gamma-sin(alpha+beta+gamma)=4sin((alpha+beta)/(2))sin((beta+gamma)/(2))sin((gamma+alpha)/(2))

|(sin alpha, cosalpha,sin(alpha+delta)),(sinbeta, cos beta,sin(beta+delta)),(singamma,cosgamma,sin(gamma+delta))|=

If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma, then which of the following is/are true:- (a)cos(alpha-beta)+cos(beta-gamma)+cos(gamma-delta)=-3/2 (b)cos(alpha-beta)+cos(beta-gamma)+cos(gamma-delta)=-1/2 (c)sumcos2alpha+2cos(alpha+beta)+2cos(beta+gamma)+2cos(gamma+alpha)=0 (d)sumsin2alpha+2sin(alpha+beta)+2sin(beta+gamma)+2sin(gamma+alpha)=0

cos (alpha + beta) cos gamma-cos (beta + gamma) cos alpha = sin beta sin (gamma-alpha)

Prove that |[cos alpha cos beta, cos alpha sin beta , sin alpha],[-sinbeta,cosbeta,0],[sinalpha cosbeta, sinalpha sinbeta, cos alpha]|=cos2alpha

Show that |[sinalpha, cosalpha, cos(alpha+delta)],[sinbeta, cosbeta, cos(beta+delta)],[singamma, cosgamma, cos(gamma+delta)]|=0

Prove that det [[sin alpha, cos alpha, sin (alpha + delta) sin beta, cos beta, sin (beta + delta) sin gamma, cos gamma, sin (gamma + delta)]] = 0

Show without expanding at any stage that: | (1,cosalpha-sinalpha, cosalpha+sinalpha),(1,cosbeta-sinbeta,cosbeta+sinbeta),(1, cosgamma-singamma,cosgamma+singamma)| =2 |(1,cosalpha, sinalpha),(1,cosbeta, sinbeta),(1,cosgamma,singamma)|